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THE MODALIST 



OR 



THE LAWS OF KATIONAL CONVICTION 



A TEXT-BOOK 



FORMAL OR GENERAL LOGIC 



by/ 

\/ 

EDWARD JOHN HAMILTON, D.D. 

h 

Albert Barnes Professor of Intellectual Philosophy in Hamilton 
College, N.Y. 



>>»<< 



/ 

( I 

tow; 



BOSTON, U.S.A. 

PUBLISHED BY GINN & CO. 

1891 






|the LIBRARY 
OF C ONGR ttSI 

WASHINGT ON 

Copyright, 1891, 
By EDWARD JOHN HAMILTON. 



All Rights Reserved. 



Typography by J. S. Cushing & Co., Boston, U.S A. 
Presswork by Ginn & Co., Boston, U.S.A. 



PREFACE. 



This text-book was written under the conviction that the 
most useful instruction is that which is enforced by the most 
thorough explanations. It is an attempt to connect the for- 
mulas of logic with principles, the ultimate character of which 
will become evident to the faithful student. Besides, the 
author had an ambition to add something to the science by 
giving permanent form to views which have been held and 
taught for years. 

Logical doctrine and praxis do not now have that place in 
education which they once had, when the university curriculum 
was chiefly occupied with the literature and the philosophy of 
the ancients. But we do not complain of this. Logic receives 
a fair share of attention in our colleges. In almost all of them 
it is a required study for at least one term ; while the larger 
institutions offer advanced courses in theories of knowledge 
and belief. 

This is all that could be expected. A pretty thorough 
indoctrination in logic can be effected in connection with forty 
or fifty class exercises ; and half as many might suffice for 
imparling the rudiments. Or may we say that the minimum 
of required work should include not less than thirty recita- 
tions, or class-exercises ; after which the young men might 
be left to their own election as to the further prosecution of 
this study? 

So far as we know, Logic is never taught without the help 
of a text-book ; though professors differ in the degree of their 
reliance upon this aid. The writer, who has used successively 
a considerable number of books, has always found it advan- 
tageous to select, with some freedom, the more important 



iv PBEFACE. 

chapters, as subjects of recitation ; aud has supplemented the 
instruction thus given by a few informal lectures, and by some 
work required of every member of the class. He has also, of 
course, encouraged the students to read more than was im- 
peratively prescribed. 

He proposes now — so far as there may be need — to deal 
with his own book as he has dealt with those of others. For 
the chapters of the "Modalist" are of such a construction as 
to facilitate this method of procedure. They will be found to 
have so much independence of one another, that almost any 
of them could be omitted while the rest would remain compre- 
hensible. And this is especially the case with certain chap- 
ters, such as the twenty-first, the twenty-second, and the 
twenty-third; in which the principles of the new analytic are 
somewhat minutely expounded. We think that a serviceable 
knowledge of inferences and syllogisms — so far as these are 
considered in existing manuals — can be obtained from chap- 
ters preceding and following those just mentioned. 

Moreover, it will be noticed that the closing sections of 
several of the longer chapters are devoted to supplementary 
discussions ; such as are consigned to small type in the author's 
metaphysical text-book. 1 In the present work this device, 
always unseemly, has not been thought necessary. The author 
is confident that any fellow-teacher who may honor him by 
employing the new logic as a means of class instruction, will 
sympathize with it sufficiently not to need specific directions 
concerning the use of it. Besides, every qualified professor 
can judge, better than any one else can, what the limitations,, 
and what the possibilities, of his work may be. 

Clinton, N. Y., Feb. 1, 1891. 

1 A volume entitled " Mental Science." 



CONTENTS. 



Prefatory Dissertation ........ 


PAGE 

1 


CHAPTER 

I. 


Logic Defined ....... 


13 


II. 


Belief, or Conviction 


21 


III. 


Logic Divided ....... 


26 


IV. 


Entities and Conceptions ..... 


31 


V. 


General and Individual Notions 


37 


VI. 


Predicative Notions; the "Categories" . 


45 


VII. 


Predicative Notions; the " Predicables " 


52 


VIII. 


The Definition of Notions ..... 


61 


IX. 


Logical Division 


71 


X. 


Propositions and Predications .... 


79 


XI. 


Categorical Predications 


89 


XII. 


The Illative Proposition ..... 


98 


XIII. 


Inferential Sequence 


107 


XIV. 


Orthologic Inference ...... 


118 


XV. 


Homologic Inference 


130 


XVI. 


Inductive Reasoning ...... 


136 


XVII. 


Hypothetical and Disjunctive Reasonings 


150 


XVIII. 


Probable Inference ...... 


162 


XIX. 


The Opposition of Propositions .... 


174 


XX. 


The Conversion of Predications 


190 


XXI. 


Contingency and Its Conversion 


204 


XXII. 


Syllogisms ........ 


222 


XXIII. 


Syllogistic Moods 


242 



VI 



CONTENTS. 



CHAPTER 

XXIV. Thf Pure, or Dogmatic, Syllogism 

XXV. The Keduction of Syllogisms 

XXVI. Fallacies 

XXVII. Fallacies in Catenate Inference 

XXVIII. Exterior Catenational Fallacies 



page 
261 

279 

290 

304 

318 



LOGIC AT THE PRESENT TIME: 

A 

PREFATORY DISSERTATION. 



One hundred years ago the philosopher of Koenigsberg, in 
the preface to the second edition of his "Kritik," declared 
that logic had not advanced a step since Aristotle, and was, in 
fact, a completed science. According to Kant, authors subse- 
quent to Aristotle had added nothing to logic, but had dis- 
figured the science by the introduction of topics foreign to it. 
" For," says Kant, " logic is a science which has for its aim 
nothing but the exposition and proof of the formal laws of all 
thought, whether it be a priori or empirical, whatever be its 
origin or its object, and whatever the difficulties which it 
encounters in the human mind." 

But, during this nineteenth century, logical questions have 
been discussed more earnestly than ever before, and, at the 
present time, no department of speculative investigation 
attracts greater interest than that relating to the laws of 
rational conviction. Differences, moreover, still prevail con- 
cerning the fundamental doctrines of this science. The only 
parts of logic on which there is general agreement are certain 
forms and rules which have descended to us from Aristotle. 
The philosophy of conviction continues a subject of debate ; 
for which reason we cannot allow that logic is a completed 
science. No science can be regarded as complete till its prin- 
ciples have been established. 

The treatise now offered to the public is the result of long- 
continued studies which have had for their object to place the 
doctrines of logic on satisfactory foundations; and it would 
be false humility were the author to conceal his assurance 
that these studies have been successful. He claims to have 



2 LOGIC AT THE PRESENT TIME: 

completed a work which Aristotle left unfinished, and that, 
too, in a way which would be approved by this great thinker 
were he now living. For Aristotle's "Organon" does not 
pretend to set forth a perfected system. It is not a treatise 
in which unity and simplicity have been reached through the 
ultimate analysis and the final synthesis of the laws of think- 
ing ; it is a collection of books written independently of each 
other, and whose discussions — especially when they relate 
to forms of argument — elucidate specific operations rather 
than universal principles. The writings of Aristotle, in gen- 
eral, reveal little effort at unification ; he aimed not so much 
to produce systems as to discover and present truth respect- 
ing important topics. Different discussions show different 
analyses of the same subject; his statements of related truths 
occasionally lack co-ordination; and he is content, at times, 
with primary and superficial generalizations. Therefore, with 
that lasting strength which results from conformity to the 
individual and the actual, his philosophy exhibits also the ob- 
scurities and difficulties and defects of uncompleted doctrines. 

We are aware that the claim to have reconstructed logic 
and to have made it a thoroughly satisfactory science is a bold 
one, and not likely to be immediately allowed. Even though 
one acknowledge his indebtedness to preceding thinkers ; with- 
out whose labors success would have been impossible; and 
though he represent himself, not as a master-thinker, but as a 
disciple who has been fortunate in his day and opportunities, 
the author's estimate of his work will be received by many 
with incredulity and by some with ridicule. Yet he knows 
what he has been enabled to do; he is certain that he has 
found the truth on every important point ; and, with this con- 
fidence, he comes before the public, not at all assured of his 
immediate reception, but willing to wait, if need be, till his 
views shall be understood. 

The reader who may desire to comprehend the spirit and aims 
of the treatise now submitted to his criticism, should consider 
some problems which exercise logicians at the present time. 

First, they desire a clear definition of their science. Aristotle 
does not give any definition. That already quoted from Kant 



A PREFATORY DISSERTATION. 6 

is the one commonly found in text-books. For instance, Sir 
William Hamilton says that " logic is the science of the formal 
laws of thought, or of the laws of thought as thought." 
This definition is unsatisfactory ; it itself needs to be defined. 
One might object to it that logic does not have all thought for 
its subject, but only rational thought ; and also, that logic 
deals with rational thought not simply as such, but as the 
instrument and vehicle of conviction. We may, however, 
accept Kant's definition, provided it be taken to signify that 
logic is the science of the formal — that is, the essential and 
necessary — laws of rational conviction. For logic is a science 
which could be used by the rational beings of any universe. 

Again, the discussions of our day call for a true determina- 
tion of the sphere and scope of logic. The Kantian limitation 
of the science to the formal laws of thought is correct, if it 
be understood rightly. Pure, formal, or general logic does not 
consider those modes of enquiry or rules of procedure which 
are peculiar to any specific sphere of existence or investiga- 
tion. Nevertheless, though thus limited, logic aims to under- 
stand all those modes of mental action which reason must 
employ, under whatever constitution of things, in her pursuit 
of truth. But if this be so, not only " pure," but also " modal," 
propositions and reasonings should be considered. That is, 
those processes of thought which follow the relations of con- 
tingency and of necessity, as well as those which use only 
simple assertions respecting classes and portions of classes, 
should be studied by the logician. Especially contingent and 
probable, no less than apodeictic, conviction, must be discussed. 
For contingency and probability are not confined to a specific 
sphere of being any more than necessity and certainty. They 
belong to the nature of things, and must be found in any uni- 
verse. The fact is that problematic inference, though setting 
forth what is not necessary, is itself as necessary an act of 
reason, and as truly governed by law, as the apodeictic judg- 
ment. 

This was Aristotle's view. He devoted far more attention 
to " modal " assertions and reasonings than to the " pure." In 
proof of this it is to be noted that four chapters of that book, 



4 LOGIC AT THE PRESENT TIME: 

the "Prior Analytics," in which syllogistic moods are exam- 
ined, treat of those moods which are "pure," while fifteen 
treat of those which are "modal." But these modal syllo- 
gisms have been neglected by logicians for centuries, and of 
late years all the teachings, both of Aristotle and of others, con- 
cerning contingent and necessary sequences, have been "for- 
mally expelled from the science." In the words of Professor 
Bowen of Harvard, " The whole doctrine of modality is now 
rightfully banished from pure logic," as pertaining " not to the 
form, but to the matter of thought." "Pure" propositions 
and "pure" syllogisms, only, are considered as lying within 
the province of the logician. Thus logic has been simplified by 
the summary process of amputating its more troublesome part. 
But the question arises, < Can desirable simplicity be obtained 
by a method which is founded on error, which divorces things 
most intimately related, and which necessitates superficial and 
one-sided views ? ' Cannot the difficulties of the case be solved 
in some better way than this ? Some more natural way ? 

In this connection the name "Modalist," which has been 
given to the following treatise, may be mentioned. It is in- 
tended to indicate that the re-introduction of modality is 
characteristic of the new logic. Other features may equal 
this in importance, but none other has so evidently modified 
the rules and formulae of the science. 

A third desideratum, in order to a clear and satisfactory 
logic, is a sound system of metaphysics, or ontology. He who 
would understand thought as employed in rational conviction 
must study thought in its relation to objects. For thought, 
by reason of its very nature, corresponds to the nature of 
things; and therefore, merely as expressive of this truth, 
every thought may- be said to have objectivity, whether it have 
an object or not. Without this characteristic thought could 
not serve the purposes of knowledge, or be of any logical 
importance. Conceptions are of interest to the logician only 
so far as they may, or do, correspond with realities and set 
forth truth or falsehood about them. Correct thinking is that 
which has this correspondence, or which, in an hypothetical 
case, would have it if the antecedent supposed were a reality ; 



A PREFATORY DISSERTATION. 5 

thinking is incorrect when it is wrongly assumed to have this 
correspondence. Such being the case, the forms and sequences 
of thought, so far as it is the instrument of conviction, must 
relate to the nature and laws of things, and should be studied 
in the light of this relation. 

It cannot be said that these principles have been rejected 
by logicians ; neither can it be said that they have been ac- 
cepted and applied. Certainly their significance has not been 
realized by those who identify things with our thoughts of 
them, or who deny that thing are as we conceive them to be, 
or who say that logic is concerned with thought only and not 
with things also. 

The philosophy from which the following chapters derive 
their force has been named Perceptionalism, because it main- 
tains, from an analytic and theoretical point of view, that 
what men call their perceptions are true perceptions of those 
very things which they say that they perceive. This philos- 
ophy prizes highly the Aristotelian doctrine of " common 
sense," or " common perception/' — kolvyj aiaOrjo-Ls, — but differs 
from it in being a developed system. It was constructed 
throughout upon a critical investigation of human thought, 
but, it is to be hoped, with a more exact initial observation 
of data than seems to have attended the "Kritik" of the 
illustrious Koenigsberg professor. 

The author ascribes his success — or what he regards as his 
success — and his confidence in it, to his metaphysical prepara- 
tion. He cannot see how a satisfactory logic can be constructed 
except in connection with a sound ontology. 

A fourth requisite to the science of rational conviction, and 
one more specific than those already noticed, is an analytic 
understanding of the nature of simple judgment and of the knoivl- 
edge of fact or truth. For these are both modes of mental 
assertion, and if we use the term "judgment" in its wide 
logical sense, cognition, the initial act of knowledge, is simply 
that species of judgment which results in absolute and well- 
founded conviction. 

Both knowledge and judgment are expressed by the " prop- 
osition " in its most general assertive use ; and their radical 



<3 LOGIC AT THE PEE SENT TIME: 

nature is to be ascertained by an analysis of the simple asser- 
tive proposition. Logicians give different accounts of this. 
Aristotle says that " a proposition is a sentence in which one 
thing is affirmed or denied of another " ; Locke, that it is a 
statement setting forth the agreement or disagreement of one 
idea with another ; Kant, that judgment is the application of 
a higher conception (the predicate) to a lower conception (the 
subject). "For example," says Kant, "in the judgment 'all 
bodies are divisible,' our conception of divisible is applicable 
to various other conceptions ; among these, however, it is here 
particularly applied to the conception of 'body.'" 

All these definitions, and others which might be quoted, are 
unsatisfactory, Aristotle's, though the best, is superficial and 
specific when it should be analytic and universal. It does 
not apply to all judgments, but only to the most common class 
of assertive propositions. Moreover, it gives a logical division 
of these rather than a true definition. The correct doctrine 
affirms judgment to be the mental assertion of the existence or 
of the non-existence of something; and that there are two 
modes of judgment. For every assertive proposition is either 
a simple existential statement, in which the existence or non- 
existence of the subject is set forth, or it is a predication-proper 
— an inherential statement — in which the predicate is set 
forth as existing, or as non-existent, in its relation to some 
subject. Without this doctrine any account of the laws of 
belief and conviction must be extremely defective. 

A fifth essential in logical science is a thorough theory of 
inference and of illative judgment and assertion in general. 
Aristotle discusses only that specific mode of sequence which 
he calls the syllogism. Modern writers for the most part 
distinguish " mediate " inference — that is, the Aristotelian 
syllogism — from " immediate " inference. The latter, they 
say, derives its life from the laws of identity and of contra- 
diction ; the former, from the dictum of Aristotle, or from 
some similar principle founded on the relation of the generic 
to the specific. In addition to this they speak of hypothetical 
inference as following the law of reason and consequent. 

Nothing could be more superficial, more inadequate, more 



A PREFATORY DISSERTATION. T 

confusing, than any such analysis. Here logic must be wholly 
reconstructed. The one universal law of inference, to which 
all others are subordinate,, is that of Antecedent and Conse- 
quent. The formula "hoc est; ergo Mud est" expresses the 
nature of every illative sequence, however simple its antece- 
dent may be or however complex. 

Then there are two generic modes of inference, the orthologic 
and the homologic. In the one of these a consequent is 
inferred from an antecedent without reference to any previous 
case of similar sequence ; in the other we infer a similar 
consequent because we perceive a similar antecedent. In 
the one, following the ontological connections of the elements 
of entity, we form direct " intuitions " of things as onto- 
logically related; in the other, we infer a consequent by 
reason of the recurrence of its antecedent, on the principle 
that like logical antecedents — whether ontological or cos- 
mological — are invariably followed by like consequents. This 
law — the homologic principle — supports not only induction, 
but all principiation whatever. It is the basis of all reasoning 
either to, or from, or in the general ; that is, it justifies such 
reasoning. 

Further, illative propositions hold an important place in the 
philosophy of ratiocination. Such propositions, whether they 
be pure or modal, are modal in meaning, and really express 
inference. They must be contrasted with simple factual asser- 
tions, whether singular or general. The subject of an illative 
predication sets forth an antecedent ; the predicate — or rather 
the predicate part of the assertion — sets forth the consequent. 
When Kant says " body is divisible," he expresses the general 
sequence that " if there is a body, it can be divided." When 
the statement, " some snakes are venomous," is used as a prin- 
ciple in reasoning, this proposition, though "pure" because 
factual in form, is illative in force, and really signifies, " if 
there be a snake, it may be venomous." 

The doctrine of the illative — or inferential — proposition 
bears directly on that of the Aristotelian syllogism. For that 
syllogism is best explained as the combination of two illative 
propositions so as to produce a third. 



8 LOGIC AT THE PEE SENT TIME: 

Sixthly, as already suggested, there is need that contingent 
as well as apodeictic inference should be analytically explained. 
This has not yet been done, because the metaphysical grounds 
of contingency have never been accurately determined. Aris- 
totle distinguishes contingency from necessity, and analyzes 
many reasonings from contingent premises, but he develops 
no theory concerning contingent sequence — its nature, its 
origin, its diverse modes, and its relations to sequences in pos- 
sibility, probability, and necessity. Nor has any one else given 
this topic thorough treatment. It is to be allowed, only, that 
the subject of probability has been handled by modern mathe- 
maticians with great ability, and that, in this way, some light 
has been thrown on the theory of problematic sequence in 
general. 

Logical possibility — possibility in the widest sense — is 
the basis of contingency and of probability. The law of this 
mode of sequence is that a thing is possible when one or more 
of its conditions exists. By condition we mean a necessary con- 
dition, a sine qua non. Space, time, and an adequate cause 
were conditions of the universe. Building materials, a builder 
and his tools, his plans and his remuneration and other in- 
ducements, are conditions of a house. Now whatever either 
is or contains a condition renders the thing conditioned possi- 
ble, so far as that condition is concerned. 

Conditions are either causal, or constitutive, or concomitant. 
The first of these enter into and compose the essential cause 
of a thing ; the second constitute its nature ; the third are its 
necessary attendants and consequents. Space, Time, and the 
Creator are free from causal conditions. 

This doctrine of conditions is the key to the philosophy of 
problematic sequence; and explains apodeictic sequence also. 
For, whenever a thing exists, then each of its conditions must 
exist, as above, in the cases of the universe and the house. 
Moreover, though conditions, as such, do not necessitate, but 
are necessary, they may be said to have a necessitative ten- 
dency or value. For the core, or vitalizing part, of any ordi- 
nary logical necessitant is composed of necessary conditions 
of the consequent. 



A PREFATORY DISSERTATION. 9 

This core is the exact logical antecedent of the consequent, 
and may be called its necessitant condition, because it both 
necessitates and is necessary. Whenever an antecedent is 
constituted exclusively from necessary conditions, it recipro- s^ 
cates with its consequent, and may be inferred from it con- 
versely. If either antecedent or consequent exist, the other 
must exist also ; and if either be non-existent, the other must 
be non-existent. The occurrence of such reciprocations is 
especially noticeable in mathematical sequences. 

A given collection of circumstances — or a case — may con- 
tain a set of conditions capable of being filled out in any one, 
but in one only, of a limited number of ways so as to constitute a 
necessitating condition. When we know that there will thus 
result an antecedent of necessity in some one way, and have no 
reason to suppose that this will occur in one way rather than 
in another, we call each of the possible consequents a chance, 
and we say that the chances are equal to one another ; because 
we divide among them the confidence of certainty. Then, 
should a proportion of these chances support some general 
specific consequent, we say that this consequent has a prob- 
ability expressed by the ratio of the chances for it to the 
whole number of chances. The probability that an odd num- 
ber will turn up on one cast of a die is one-half, because three 
out of the six possible individual consequents favor an odd 
number. 

Now, when we know only that a certain specific consequent 
is supported by chances and are unable to determine the ratio 
of the chances for it to the whole number or to those against 
it, then the indeterminate probability thus arising is that con- 
tingency — or contingent sequence — of ivhich logic treats. 

A most important modification of contingency takes place 
when it is guarded against a necessity of the opposite. This is 
effected either when the consequent asserted as contingent is 
known to have already sometimes accompanied the antecedent, 
or when the very nature of the antecedent is seen to preclude 
impossibility. "Man may be wise" is guarded against a 
necessity of the opposite because men have been wise. This 
renders it clear that further investigation will not show that 



10 LOGIC AT THE PRESENT TIME: 

man (as such) cannot be wise. So also ace certainly may 
turn up on the cast of a die, because there is nothing in 
the nature of a die or in the act of throwing it to prevent 
ace appearing. 

Another mode of contingency which is not guarded is fre- 
quently used by the mind. But guarded contingency is that 
assumed in the modal syllogisms of Aristotle, and has a just 
pre-eminence. 

The theory of sequence based on th Doctrine of Conditions 
renders possible a simple and intelligible account of modal 
reasoning, and, indeed, makes the modal syllogism, in its apo- 
deictic and its contingent moods, the syllogism par excellence, 
and that to which all syllogizing must be referred. Thus, too, 
what has long been the terror and despair of scholars has been 
converted into the crowning part of logical science. 

Once more, and in the seventh place, we may say that the 
Aristotelian syllogism calls for more accurate definition than it 
has yet received. The ordinary description of it as the 
" mediate inference " is indefinite and unsatisfactory, and the 
explanation of its process as the comparison of two terms, or 
two ideas, with a third so as to determine their relation to 
each other, is a vague, inadequate attempt at the expression of 
truth. Aristotle himself says that " a syllogism is a sentence 
in which, certain things being laid down, something else dif- 
ferent from those things necessarily follows by reason of their 
existence." This, also, is superficial and inadequate. For the 
questions arise, ' What is the nature of the things laid down ? 
and what is the nature and ground of the sequence ? ? There 
is a lack here similar to that in Aristotle's definition of the 
proposition. 

The only mode of inference which possesses all the "acci- 
dents " of syllogistic figure and mood — the only style of 
sequence to which all the rules of syllogizing apply — is that 
which combines two general illative propositions so as to produce 
a third : it is the process which obeys the law that the ante- 
cedent of a second antecedent is antecedent also of the second 
consequent; or (from another point of view) the law that the 
consequent of a prior consequent is consequent also of the 



A PREFATORY DISSERTATION. 11 

antecedent of that prior consequent, and is therefore a " con- 
sequent-consequent." 

We cannot now speak further of this law or of its relations 
to other principles of inference. Our present object is not to 
expound the new doctrines, but only to indicate their nature. 
We must, however, add that no change has been proposed in 
those forms and rules of syllogizing which have come down 
to us from ancient times, except in the way of unification and 
of a slight addition. After the nineteen commonly recognized 
syllogistic moods have been interpreted by modal laws, twelve 
other moods, very simple in structure, have been added so as 
to express conjectural, or unguarded, sequences in contingency. 
Thus every mode of syllogizing used by the mind has been 
provided for. These unguarded moods are equal in philosophi- 
cal, though not in dialectic, importance to those ordinarily 
allowed ; they have been neglected heretofore. Some of them 
indicate methods of reasoning which are quite common. 

One result of the new analysis has been to exalt the general 
doctrine of inference and its modes above that of the Aris- 
totelian syllogism. The sphere of the latter has been restricted 
to "general catenate inference"; while other specific modes 
of sequence have been assigned distinctive places. This but 
carries out a tendency in modern logic, according to which 
various modes of inference have been treated independently 
of the syllogism and as following principles of their own. 

Even yet, however, logicians do not make sufficient allow- 
ance for the fact that different modes of inference may employ 
the same linguistic expression. A verbal, or superficial, form 
of sequence should not be taken as the ultimate explanation of 
inferences essentially diverse. Logical theory should not rest 
in the secondary and the ministerial, but should point directly 
to the ultimate. Following this rule, the Aristotelian syllogism 
will be given a true pre-eminence, yet also a definite and limited 
place, among modes of inference. 

In the foregoing remarks no enumeration of new doctrines 
has been attempted. This preface is intended merely to show 
the spirit and aim of the treatise which it introduces. Possibly 
other teachings of the book may seem to some of greater inter- 



12 LOGIC AT THE PRESENT TIME. 

est than those already referred to. But this may be said re- 
garding every doctrinal modification : it has been introduced 
without any love for novelty, and only under a sense of neces- 
sity, and with a profound confidence in that underlying system 
of philosophy which has suggested the innovation. The posi- 
tions taken relating to logical definition and division — to the 
categories and the predicables of Aristotle — to induction — 
and concerning probable judgment — the specific laws of 
orthologic sequence, whether mathematical or metaphysical — 
the specific modes of homologic sequence — the quantification 
of terms in propositions — the opposition and conversion of 
predications — and concerning fallacies and their classification, 
have all been controlled and determined by the analysis of 
Perceptionalism. 

We would say, in conclusion, that, in one respect at least, 
the aim of the present work has been very limited. The 
history of opinions and the discussion of views which are well 
worthy of attention, have been quite beyond its scope. The 
endeavor has been simply to elaborate fundamentals. Perhaps, 
after a time, some additional chapters may be composed in 
criticism of important theories and in further elucidation of 
the system now submitted. 

Hamilton College, Clinton, N.Y. 

Nov. 4, 1800. 



THE MODALIST: 

OR, 

THE LAWS OF RATIONAL CONVICTION. 
CHAPTER I. 

LOGIC DEFINED. 

1. Origin of the name. 2. Not the science of "thought as thought," nor 
of "inference" only. 3. The science of rational conviction. 4. Reason 
not radically different from lower faculties, but a special endowment and 
development. 5. " Discursive " reason is articulate and intentional; 
"intuitive" reason, habitual and instantaneous. 6. Truth is (a) attri- 
butal, (6) objectual, (c) subjectual, or propositional. The term "subject." 

1. The name "Logic" was originally the Greek adjective 
corresponding to the nonn Aoyos, which noivn signifies either 
language or that rational and elaborated thought of which 
language is the expression. As descriptive of a science the 
adjective AoyiKo? was employed either in the singular or in the 
plural. The plural phrase, ra XoytKa, might be translated 
" the principles of rational thought." It sets forth the science 
as composed of parts. It is similar in origin to the expression, 
to. fieTa<f>vaiKd, or " metaphysics," a name anciently given to the 
philosophy of the ultimate in conception and in existence. 

The singular designation, "tj Aoyi/oj," is that Anglicized 
by the word " logic." The meaning of it is fully expressed in 
the original language by adding to it a noun, either eVtorrT/^ 
or re^vr)-, and the phrase thus formed may be translated "the 
science, or the art, of rational thinking." The term t£xvv] with 
the Greeks, like the term "art" with us, is often used to 
designate a practical science. Logic even yet is sometimes 
13 



14 THE MODALIST. [Chap. I. 

called an art because it not merely elucidates truth, but also 
formulates rules and gives useful directions. 

2. This science has been variously defined by modern writers. 
Most of them say that " Logic is the science of the laws of 
thought," and some make this statement emphatic by saying 
" of thought as thought " ; that is, of thought considered 
simply, or chiefly, as to its own nature. One great objection 
to this definition, at least as it is commonly given, is that it 
uses the word " thought " in a narrow and technical sense with- 
out sufficient explanation. This word is applicable to all our 
thinkings as well as to those exercised in connection with 
rational conviction. Memory, imagination, sense-perception, 
consciousness, have each its own mode of thought ; to say 
that logic is the science of thought without showing clearly 
what kind of thought does not satisfy the enquiry of the 
mind. 

But a second and more serious fault in the above-men- 
tioned definition is that it tends to conceal a radical distinction 
of mental science, namely, the distinction between thought, or 
conception, and belief, or conviction. This tendency is especially 
noticeable when we are told that Logic is the science of thought 
as thought. For, according to the most natural use of terms, 
Logic does not consider thought simply as thought, but thought 
always and only as the instrument and vehicle of conviction ; 
and the laws of thought as the organ of belief cannot be clearly 
understood if we do not first recognize the distinction between 
thought and belief. 

Again, some have defined Logic as the science of reasoning, 
or inference. For instance, Professor De Morgan calls it "the 
calculus of inference necessary and probable." This definition 
is not sufficiently broad ; Logic discusses not only inferences 
and reasonings, but also conceptions, or notions, and statements, 
or propositions. Nor are these considered merely in subordi- 
nation to reasonings, but also as having an independent use of 
their own. An important part of Logic aims simply to render 
our notions and statements more adequate and efficient as the 
embodiments of truth. 

Another class of writers, desiring to emphasize the practical 



Chap. I.] LOGIC DEFINED. 15 

office of Logic, say that it is the science which teaches "the 
right use of reason." This definition cannot be greatly con- 
demned, yet is wanting in completeness. The rules and direc- 
tions of Logic as an art cannot profitably be separated from 
the philosophy of our rational operations. To say merely that 
Logic teaches the right use of reason is not a sufficient recog- 
nition of that scientific spirit without which any logical sys- 
tem would be weak and lifeless. Moreover, the term " reason," 
when used without qualification, covers a wider ground than 
is surveyed in logical discussions. In particular, that construc- 
tive imagination which produces poems and works of fiction is 
something pre-eminently rational ; yet it does not fall within 
the cognizance of the logician. 

3. Perhaps the defmiteness of conception for which we have 
been seeking may be obtained in connection with the following 
statement : Logic is the science of the operations and products 
of the rational faculty in the pursuit and use of truth. 

The distinction, incidentally assumed in these words, between 
the operations and the products of the mind is worthy of some 
attention, because it differs from that existing between material 
products and the labors in which they originate. In the latter 
case the things distinguished are of totally diverse natures, 
whereas the mental conception or conclusion, which results 
from some rational process, is a thing of essentially the same 
kind with the steps which lead to it. It is simply a completed 
thought or conviction which the memory retains, and which 
the mind can recall and use. Hence, after a mental product 
has been formed, it may immediately become part of a process 
which aims at a further product ; as, for instance, when one 
notion, after being denned, is employed in the definition of 
another. 

But the important point in our conception of Logic is, that 
this science considers reason, or the rational faculty, only so 
far as it is engaged in the pursuit and use of truth. On this 
account, if brevity were desired, it might be sufficient to say 
that Logic is the science of rational conviction ; for belief, or 
conviction, is always the apprehension by the mind of some- 
thing as true. That such is the essential character of Logic 



16 THE MODALIST. [Chap. 1. 

will be evident to any one who may examine the various sys- 
tems of doctrine which have gone under this name. 

At the same time Logic is not the science of conviction in 
general, but only of those modes of conviction which depend 
on the exercise of the reason. Those cognitional convictions, 
which are not of a rational origin, though recognized by the 
logician, have only a preparatory and subordinate place in his 
discussions. One knows, from consciousness, of the pleasure 
experienced in meeting with a friend, or, from sense-perception, 
of the size, weight, solidity, roughness, and coldness of a stone ; 
but such cognitions are not exercises of the reason, and are not 
investigated by the logician. This is true also of those per- 
ceptions of times, distances, changes, and relations which ac- 
company the operation of sense-perception and consciousness. 
Without any rational process, a person holding two stones, 
one in each hand, would know that they exist contempora- 
neously, that they are separate in space, that they are similar 
to one another, that the one is heavier or rougher than the 
other, and so on. In short, all presentational cognitions, and 
the memories consequent upon them, are presupposed or taken 
for granted, in the science of rational conviction. 

In speaking of Logic as a science, we would not ignore those 
practical aims, on account of which it has been called an art. 
Some authors have discussed logical questions in a purely the- 
oretical spirit and without any attempt at useful directions. 
In this they deviate from that conception of the science which 
the experience of past times has shown to be both reasonable 
and advantageous. 

4. Accepting the definition that Logic is the science which 
discusses the operations of reason in the pursuit of truth, let 
us consider attentively two leading ideas contained in it ; let 
us determine exactly what we mean by reason and truth. 

Reason, or, as it is sometimes called, the rational faculty, is 
a development of intellectual power which, because of its great 
importance and wonderful accomplishments, is distinctly no- 
ticed and named ; yet it is not a faculty radically different in 
nature from our lower mental capabilities. A man of genius 
differs from his fellow-men, not in the nature of his gifts, but 



Chap. L] LOGIC DEFINED. 17 

in the natural strength of them and in the degree of their 
development. In like manner, reason is to be distinguished 
from those powers of mind which man has in common with 
the more intelligent brutes rather as a special endowment of 
strength than as a faculty of a distinct nature. When Locke 
speaks of " that faculty whereby man is supposed to be distin- 
guished from the beasts, and wherein it is evident that he 
much surpasses them," his words must be received with care. 
Examination shows that reason is not a faculty separate in its 
nature from our other powers, but only a special endowment 
of intellectual ability. The perceptions of sense, no less than 
those of the rational faculty, employ notions, judgments, and 
inferences; but reason far transcends all sense-perceptions in 
the grasp of her apprehension and understanding. In like 
manner, there is an exercise of the faculty of reasoning, or 
ratiocination, which falls far short of what we call reason. 
Many brutes exhibit some power even of connected reasoning. 
Eeason is that gift by which man is capable of language, of 
civilization, of material social and intellectual progress, of civil 
government and laws, and of moral and religious life. 

The superiority of this endowment to the lower powers of 
mind is manifested principally in two particulars. In the first 
place, rational conceptions are peculiarly comprehensive ; and 
secondly, resulting in part from this comprehensiveness of 
conception, rational judgments are peculiarly penetrative. Eea- 
son can seize and hold under consideration many things at 
once, so as to consider fully their nature and relations ; and, 
while doing so, she reaches a knowledge of things which are 
invisible to lower powers of thought. So far as sense-percep- 
tion is concerned, a brute sees the different parts of a locomotive 
as well as a man ; but no brute can understand the relations, 
use, and value of each part, and by what process the whole 
contrivance accomplishes its work. Eational intelligence not 
only perceives these things, but constructed a locomotive in 
thought before such an invention ever existed. 

Philosophers agree that, in the human mind at least, reason 
is exercised in two modes, the intuitive and the discursive, but 
they differ concerning the way in which these modes of reason 



18 THE MOBALIST. [Chap. 1. 

are related to one another. Some hold that rational intuition 
is entirely without a process, or, at all events, wholly different 
in nature from rational discourse- The better opinion is that 
the intuition of reason is an instantaneous action the rapidity 
of which, resulting from the habitual and spontaneous use of 
certain modes of apprehension, causes the steps of the process 
to escape detection. Believing this, we must hold the intuitive 
reason to be a faculty of a very different nature from that 
power of " intuition " by which necessary relations are imme- 
diately perceived, and which enters as an element into every 
phase of human cognition. 

The discursive mode of reason is that ordinarily employed 
in all our deliberate investigations. It is distinguished from 
the intuitive by being more analytical, articulate, and con- 
secutive, and in being immediately under the guidance of 
the will. This form of the faculty, also, is the proper subject 
of logical principles and rules, because it alone admits of 
direct self-inspection and regulation. Yet an understanding of 
" the discourse of reason " enables us to understand " the intui- 
tion of reason," as well ; the two being radically of the same 
nature. The rapid mode of reason may be compared to that 
motion of spinning or weaving machinery which is too swift 
for observation : the more deliberate mode may be likened to 
the working of a type-writer or a telegraphic instrument, every 
movement of w T hich is an intentional act of the operator. The 
intuitive mode becomes understood when the same conclu- 
sions to which it comes quickly are reached by the consciously 
directed methods of mental discourse. 

5. The question, " What is truth ? " was often asked by 
ancient philosophers, and with them it mostly had a moral 
significance and meant, " What is the true end of life ? " The 
first aim of the thinkers of antiquity was to find some essential 
principle the knowledge and observance of which might lead 
men to true happiness. In modern discussions, the term 
"truth" is more commonly used in that primary and literal 
sense which it has when we say that a statement is true, or 
is a truth, and deny that it is false. The truth thus mentioned 
has been called intellectual truth, and has been distinguished 



Chap. I.] LOGIC DEFINED. 19 

in this way from that more specific kind which is ethical or 
moral. For truth in general and by reason of its essential 
nature is closely related to intellect. 

This intellectual truth is of three modes, or denominations, 
which are intimately connected with one another. First, there 
is attributed truth. This is that defined by St. Thomas Aquinas 
when he says, " The truth of thought is a correspondence of 
thought and fact according to which thought says that what 
is, is, or that what is not, is not." (Veritas intellectus est 
adaequatio intellectus et rei, secundum quod intellectus dicit 
esse quod est, vel non esse quod non est.) Evidently if a 
statement — for example, that "the man is rich " — be true, there 
is a fact existing outside of one's thought, and also a proposi- 
tion within the mind corresponding to the fact ; and the truth 
which we ascribe, or attribute, to the proposition, lies in this 
correspondence. 

Again, there is objectual truth. This is not any correspond- 
ence, but it is the fact, or reality, which is the object of the 
mind's knowledge, and which corresponds to the proposition 
in the mind. Accordingly we sometimes say, "That is the 
truth," our meaning being, " That is the fact." In such lan- 
guage fact, as the basis and object of knowledge, is called 
truth. 

Finally, there is subjectual, or propositioned, truth. The 
term "subject," when opposed to the term "object" in 
modern philosophy, signifies the mind as the subject of im- 
pressions from objects and of ideas about them. Subjectual 
truth, accordingly, is the ideas or conceptions of the mind 
considered as corresponding with facts or objects known. 
This may also be styled propositional truth, because when 
expressed fully it assumes the form of the assertive propo- 
sition. 

For belief, or conviction, cannot be exercised on the mere 
conception of a thing as to its nature, however correct and 
complete this conception may be. There is always need that 
we should conceive of a thing as existing or as non-existent. 
To believe in God is to believe in the existence of God, or in 
the proposition that God exists ; to believe in the justice of 



20 THE MODALIST. [Chap. I. 

God is to believe in the existence of His justice, or in the 
proposition that God is just; and to disbelieve in God and 
His justice is to believe that they do not exist. It is because 
assertive propositions set forth things either as existent or as 
non-existent that they are naturally fitted to express subjectual 
truth. 

The signification of the noun " subject," referred to above in 
connection with the adjective "subjectual," belongs chiefly to 
the discussions of psychology. It is to be distinguished from 
the ordinary meaning of this word in Logic, according to which 
it is opposed, not to the term "object," but to the term "pred- 
icate." In the distinctively logical sense a subject is anything 
whatever of which anything may be affirmed or denied. But 
the doctrine of truth pertains to philosophy in general, not to 
Logic only; and therefore we need not confine ourselves, in 
the statement of it, to strictly logical terms. 

When we say that Logic considers the operations of the 
reason in the pursuit and use of truth, it is clear that the ref- 
erence is to subjectual, or propositional, truth. This is that 
which the mind immediately apprehends and employs ; it is 
only by obtaining possession of this that the mind becomes 
sensibly related to attributal and objectual truth. 



C.iap. II.] BELIEF, OR CONVICTION. 21 



CHAPTER II. 

BELIEF, OK CONVICTION. 

1. The two primary powers of mind, — thought, or conception, and 
belief, or conviction. 2. Belief and knowledge defined. 3. Judgment 
and cognition defined. 4. Inferential judgment, (a) either apodeictic 
or problematic, (b) either actualistic or hypothetical. 5. The sphere of 
general, or "pure," logic. 

Thought, or conception, and belief, or conviction, may be 
termed the primary powers of the intellect, because, in their 
exercise, the work of mind is directly accomplished : our other 
powers, such as attention, association, abstraction, generaliza- 
tion, synthesis, and analysis, are secondary, because their 
function is to modify the operation of thought and belief. 

1. Of the two primary powers, thought is the more promi- 
nent in our experience ; for belief is felt only as an accompa- 
niment of thought. We may have conceptions unattended by 
convictions, but we cannot have a conviction except as attached 
to some conception. Moreover, in every enquiry respecting 
belief, questions respecting the origin and mutual connections 
of our thoughts are implicated. This close association of 
belief with thought has led many writers to treat belief as 
if it were merely a peculiar, or, it may be, a superior, kind 
of thought. This is a mistake, and the cause of wide-spread- 
ing confusion. President McCosh ("Scottish Philosophy," 
p. 384) says truly, "Belief should have a separate place in 
every system of psychology " ; to which we add, " and in every 
system of logic also." 

2. But, before proceeding farther, we must remark that, in 
the present discussion, the term "belief" is used in a very 
wide sense. Ordinarily belief signifies a mode of mental con- 
fidence which falls short of knowledge, yet which is greater 
than mere guess-work or presumption. Seeing certain weather 
indications, one might say, " I believe, though I do not know, 



22 THE MOBALIST. [Chap. II. 

that it is going to rain." We now include under belief every 
degree of confidence respecting the truth of a thing from the 
weakest conjecture to the most absolute assurance. According 
to this signification knowledge is a kind of belief ; for knowl- 
edge is absolute and well-founded certainty. 

At present, also, we use the term " conviction " as synony- 
mous with " belief," though conviction strictly indicates belief, 
not simply, but as founded on evidence. In like manner, we 
employ the terms "conception" and "thought" interchange- 
ably, though a conception properly signifies a thought formed 
synthetically. 

The most important point in the doctrine of belief is, not 
that conviction takes place only in connection with conception, 
but that belief is possible only when the thought of existence 
or that of non-existence is united with or included in our con- 
ception of a thing. This truth has been expressed too strongly 
by those who say that belief takes place only in connection 
with propositions. It is the essential and formal function of 
propositions to set forth things as existent or as non-existent, 
but any notion may become matter of belief if it only be an 
existential conception; that is, if it have, as one of its ele- 
ments, the thought of existence or that of non-existence,, 
whether this element be prominent in our conception or not. 
For instance, should one predicate something respecting an 
existing object, saying, "My friend is faithful," the subject- 
notion, "my friend," presents the object as existing, and as 
believed in, though the existence directly asserted by the propo- 
sition is not that of the friend, but of his faithfulness. 

3. The same necessity which leads to a wide use of the term 
" belief " calls for an equally broad use of the term "judg- 
ment"; for judgment is the initial act of which belief is the 
permanent and reproducible product. Ordinarily judgment 
signifies the formation on evidence of a probable conviction. 
Hence Locke says, "The faculty which God has given to man 
to supply the want of clear and certain knowledge is judgment, 
whereby the mind . . . takes any proposition to be true or false 
without perceiving demonstrative evidence in the proof." But 
logicians have found it advantageous to give the name " judg- 



Chai>. II.] BELIEF, OR CONVICTION. 23 

ment " to the assertive faculty in general ; in other words, to 
that faculty, in the exercise of which we form convictions of 
any kind, and are led to embody these convictions in propo- 
sitions or statements. According to this use of language cog- 
nition, the initial act of knowledge, is a mode of judgment, 
knowledge being, as we have seen, a mode of belief. 

If we consider our convictions and the judgments productive 
of them with reference to their primary origin and mode of 
formation, they may be divided into two classes, — the presen- 
tational and the inferential. The former of these includes our 
cognitions of such things and relations as are immediately 
present to the soul in space and time ; and with these cogni- 
tions we may also classify, as things of the same logical re- 
lations, the simple reproductions of presentational perceptions. 
Our first perceptions are important because they are the basis 
of all subsequent knowledge and belief, but the special con- 
sideration of them belongs to psychology. They furnish those 
materials of fact which reason uses, but are not themselves 
distinctively rational. While, the logician recognizes them, he 
does not make them the subjects of his investigation. 

Inferential convictions are those which assert the existence 
or the non-existence of things not immediately present to the 
soul. It is with them that the discussions of logic are chiefly 
occupied. They differ from presentational cognitions in that 
the latter do not depend on any previous knowledge, while 
inference assumes something as already known to be fact, and 
then asserts some second thing as a fact connected with the first. 

4. Considered with reference to their own nature and opera- 
tion, inferential judgments are divisible into two principal 
classes, — the apodeictic, or demonstrative, and the problematic, 
or contingent. 

The apodeictic inference leads to an absolutely certain con- 
clusion, and excludes the possibility of a thing being otherwise 
than as it is shown to be. Such are mathematical demonstra- 
tions and all reasonings which infer things as necessarily related 
to given fact. When a surveyor knows the length of the sides 
of a field and the angular measurements of its corners, he 
calculates the area by an apodeictic, or demonstrative, process. 



24 THE MODALIST. [Chap. II. 

Problematic inference is based on the consideration of things 
as possible or as contingent, and produces forms of conviction 
weaker than those which result from demonstration. Contin- 
gency is a mode of sequence approaching probability : it is an 
expectant possibility. It arises when an antecedent of possi- 
bility admits only a limited number of possible consequents, 
some one of which must be realized. Old age is one of several 
conditions, one or other of which must belong to every man. 
Therefore it is contingent to man to be old. 

Contingency is best discussed as a mode of possibility which 
prepares for probability. Many, following Aristotle, and neg- 
lecting the distinction between contingency and probability, 
treat both modes of sequence under the head either of contin- 
gent or of probable inference ; but a wise use of terms limits 
" contingency " to those cases in which a thing is looked for, 
or in any degree expected, as possible, without having its 
probability determined, and limits " probability " to those 
cases in which some proportion out of a total number of 
chances is found or estimated to favor some conclusion. Thus 
it would be a judgment of contingency to say, " A merchant 
may prosper, and become wealthy " ; but of probability to say, 
" The wise and prudent merchant will prosper." Contingency 
lies between possibility and probability, being more than the 
one and less than the other. It passes into probability when- 
ever the ratio of the chances is estimated. Both contingency 
and probability expect, which accounts for their being often 
included under the general name " contingency " ; but they are 
clearly distinguishable. 

Another division of inferential judgments separates them 
into the actualistic and the hypothetical. This distinction relates 
not so much to the internal nature and operation of inferences 
as to the character of the grounds on which they are based, 
and of the convictions which they produce. For when an 
inference, whether apodeictic or problematic, arises from our 
knowledge of fact or from belief in what we take to be fact, 
the conclusion of it asserts fact, or at least the possibility or 
probability of fact ; and the inference is actualistic. But if 
our reasoning be based on supposition or assumption, the con- 



Chap. II.] BELIEF, Oli CONVICTION. 25 

elusion sets forth only what would be fact (necessarily, or 
possibly, or probably), provided the supposition were realized. 
In this case the inference is hypothetical, and asserts what, in 
the most literal sense, may not be true at all. Should we sup- 
pose one of the Green Mountains to be of solid gold, we might 
assert Vermont to be the wealthiest State in the Union, and 
the inference would be correct ; yet evidently neither premise 
nor conclusion Avould set forth reality. 

Hypothetical inferences may be based on antecedents to 
which no facts ever correspond, but more frequently they pre- 
sent the abstract operation of some law of existence or of 
nature. For it is only by an exercise of the imagination that 
we can conceive of the separate working of a law which never 
is seen to operate except under a complication of modifying 
circumstances. Hence hypothetical inferences are largely 
employed in science. 

5. Some writers teach that neither the inference of the 
actual nor that of the probable or of the contingent lies within 
the sphere of logic. Rightly conceiving of logic as the general 
science of our rational operations and as independent of any 
particular branch of knowledge, they say that the theory 
either of problematic or of actualistic conviction is necessarily 
connected with that knowledge of specific classes of things 
which experience gives us, and that the logic of hypothetical 
demonstration, alone, is an abstract and ontological science. 

These views are not well founded. While all the methods 
of reason should be illustrated and tested by their application 
to particular cases, the principles of actualistic conviction are 
not specially connected with any one class of facts or objects, 
and those of problematic inference are such as must govern 
finite intellects in their judgments relating to any universe, 
or system of affairs, in which they can be placed. If the sub- 
ject of logic as a general science — of "Pure Logic," as it has 
sometimes been called — be rational conviction in general, then 
logic must consider actualistic as well as hypothetical, and 
problematic as well as apocleictic, inference. All these modes 
of rational conviction, together with their principal varieties, 
are such as must be followed, by minds like ours, in any uni- 
verse, or system of things, whatever. 



26 THE MODALIST. [Chap. III. 



CHAPTER III. 

LOGIC DIVIDED. 

1. Logic is objective or subjective. 2. Is general, or abstract, and 
special, or applied. 3. Is "pure," or "formal," and mixed, or modified — 
but ambiguously. 4. The terms "directive" and "corrective" proposed. 
5. Logic concerns («) notions, or conceptions, (p) judgments, or assertions, 
(c) inferences, or reasonings. 

In order to render our conceptions of logic and of the sphere 
of its instructions more definite, various distinctions and divis- 
ions have been made. 

1. First, objective has been distinguished from subjective logic, 
or, in the language of the schools, Logica Systematica from 
Logica Habitualis. The necessity for this distinction arises 
from the double signification of the word "art." Since this 
word may indicate either a system of practical principles or an 
acquired facility in the application of those principles, there 
are two senses in which one may be proficient in logic. He 
may be a theoretical logician, well-acquainted with the laws 
and rules of thought, or he may be a practical logician, skilful 
in the application of the rules. While habitual logic is a chief 
end of systematic logic, these two " arts " are distinct acquire- 
ments, and do not always accompany one another. He who 
would be in every sense a complete logician must not merely 
familiarize himself with the principles of correct thinking, 
but must also sedulously practise them. Nor should he expect 
to obtain from books, or even from instructors, much more 
than a useful knowledge of right methods. 

The foregoing distinction has sometimes been called a divis- 
ion of logic. But it does not really divide the science. It 
only explains how the term " logic " may be employed in a 
secondary sense. Subjective and objective logic cannot natu- 
rally be regarded as parts of the same whole ; and the logic set 



Chap. III.] LOGIC DIVIDED. 27 

forth in books, which is that commonly spoken of, is wholly 
objective. 

2. Again, general, or abstract, logic has been distinguished 
from special, or applied, logic. 

Every department of enquiry is properly subject to various 
regulative principles connected with the specific character of 
its investigations ; and these principles, though immediately 
subordinate to the universal rules of right thinking, constitute 
a separate system of directions. Mathematical progress is 
promoted by a knowledge of the correct use of diagrams, in- 
struments, figures, symbols, modes of notation, and methods 
of calculation. In courts of law barristers and judges are 
governed by rules respecting the pertinency and value of dif- 
ferent modes of proof and the fair interpretation of legislative 
enactments. The theologian appeals to the canons of Biblical 
exegesis ; and the psychologist, who would ascertain the laws of 
mental life, first determines on what sources of knowledge 
and on what methods of enquiry he may rely. In short, every 
science has its own principles of procedure, which, as supple- 
mentary to the rules of right thinking in general, may be 
called the special logic of that science. 

But the several regulative codes now described are no part 
of logic in the ordinary acceptation of the word; for by 
" logic " we commonly mean that general science which sets 
forth those forms and laws which rational conviction should 
observe, no matter what may be the specific nature of the 
topics considered. The distinction between general and special 
logic is not properly a division of that general science. Each 
special logic involves considerable acquaintance with the de- 
partment of investigation to which it pertains, and is simply 
that philosophical "introduction," or "methodology," without 
which great progress can scarcely be hoped for in any branch 
of knowledge. Every such code is a valuable addition to the 
science which it is intended to promote, and should be studied 
as a part of that science. 

3. Again, pure, or formal, has been contrasted with mixed, 
or modified, logic; though logicians differ greatly in their 
explanations of this distinction. 



28 THE MODALIST. [Chap. III. 

Some say that general, or abstract, logic is " pure," because 
unmixed with the principles of any specific science, and 
" formal," because it sets forth the radical methods employed 
by reason in every sphere of enquiry ; while particular meth- 
odologies modify the general rules of reasoning by mingling 
their own directions with them, and therefore constitute mixed, 
or modified, logic. In other words, Pure, or Formal, Logic is 
just the same as General, or Abstract, and Mixed, or Modified, 
Logic is just the same as Special, or Applied. This use of lan- 
guage is quite common, and is so supported by authority that it 
cannot be condemned or avoided ; yet it is really undesirable. 
It repeats a distinction already provided for, and, as we shall 
see, conflicts with another and better use of terms. 

Again, those who hold that the " necessary " laws of thought 
pertain only to hypothetical demonstration, confine the terms 
"pure" and "formal" to apodeictic logic, and relegate to 
mixed logic the consideration of actualistic conviction, of 
probability and contingency, of doubt, and of error. This 
division of the science and the implications of it cannot be 
allowed. The theory of demonstration cannot be separated in 
this way from the rest of logic. The same immutable and 
ontological laws underlie all modes of sound judgment and 
correct inference. 

According to a third method of employing the terms in 
question, the logic of correct conviction is called " Pure," or 
" Formal," and that of imperfect and erroneous thinking, Mixed, 
or Modified. We can conceive of a purely intellectual being, 
unaffected by any cause of error, and compare him with 
creatures like ourselves who are subject to mistakes. And 
our mental action, so far as free from failure or delusion, 
might be held to obey the laws governing that pure intelli- 
gence ; while our deviations and delinquencies in the pursuit 
of truth would be accounted for by influences which mingle 
with our thinkings and lead them astray. Hence we discrimi- 
nate between the philosophy of the defective use of reason 
and that of correct and normal thinking. The distinction 
thus made is a true division of General, or Abstract, Logic. 

4. At the same time, since logicians have disagreed in their 



Chap. III.] LOGIC DIVIDED. 29 

use of terms, two new names may be of service here. Were 
we, instead of the last distinction, to designate Pure Logic as 
Directive, and Modified Logic as Corrective, and were we to 
assign to the one the perfect and normal modes of rational 
conviction, and to the other the imperfect and abnormal modes, 
all room for misapprehension would be taken away. 

But, while dividing logic into the Pure, or Formal, or Direc- 
tive, and the Mixed, or Modified, or Corrective, Ave do not mean 
to say that the discussion of correct and that of incorrect pro- 
cesses should be wholly separated from one another. Clear- 
ness of statement and an orderly arrangement of details may 
require some separation, but we must not lose that advantage 
which accrues from the immediate contrast of perfection and 
imperfection. The division of logic into the Directive and the 
Corrective is principally significant as marking two lines of 
thought which run parallel with each other in logical investi- 
gations. 

5. The distinction between actualistic and hypothetical con- 
viction, though fundamental in logic, does not yield any divis- 
ion of the science. The difference of these modes of belief, 
both as to nature and origin, is very apparent, and the forms 
and processes of thought in connection with which they are 
experienced are perfectly similar. To determine whether a 
conclusion be actualistic or hypothetical, we have only to know 
whether it be drawn from fact or from supposition. This dis- 
tinction, therefore, does not give rise to any great variety of 
discussions. 

But an important division of logic is based on those three 
radical modifications of mental action which reason employs. 
For every exercise of rational thought is either a conception, 
or a judgment, or an inference ; and every question in logic 
concerns one or other of these three things. The necessity 
of grouping according to this division soon becomes evident 
to the investigator, and it is also perceived that there is a 
natural order of succession for them, namely, that conceptions 
should be studied before judgments, and judgments before in- 
ferences. Hence most text-books contain three principal parts, 
corresponding to these three general topics. 



80 THE MODALIST. [Chap. III. 

But here we must remark that the logical division of a body 
of scientific knowledge should not be confounded with the 
orderly plan of a treatise ; though these things often go by the 
same name. The object of logical divisions is to impress upon 
us certain pervasive and fruitful distinctions ; the arrange- 
ment of a treatise is designed to facilitate our progress in the 
understanding of doctrines. Accordingly, in a scientific book, 
several radical divisions may be given, while only one arrange- 
ment of topics can rightly be adopted. From the nature of 
the case, indeed, any wise order of discussion must refer more 
or less directly to logical division, but the work of arrange- 
ment should not be so controlled by this relation as to be pre- 
vented from the free pursuit of its own proper aim. 

These remarks may be illustrated by the plan of procedure 
chosen for the present treatise. It is essentially the same 
with that commonly adopted. It is based on the division of 
our rational states into conceptions, judgments, and inferences, 
and also on the fact that the doctrine of inference calls for a 
considerable variety of discussions, and occupies an extended 
place in logic. 

Having now finished some necessary introductory disserta- 
tions we shall apply ourselves, in the next part of this treatise, 
to questions concerning conceptions, or notions. Then we shall 
take up judgments, or assertions. After that we shall discuss 
the radical laws and forms of inference ; whether they belong 
to the apodeictic (or demonstrative), or to the problematic (or 
contingent) inference. This will prepare us for the composi- 
tion of inferences and the conclusions thereby obtainable ; 
which things fall under the head of syllogisms. Finally, 
some closing chapters may be specially devoted to fallacies 
and the causes of error. 



Chap. IV.] ENTITIES AND CONCEPTIONS. 31 



CHAPTER IV. 

ENTITIES AND CONCEPTIONS. 

1. Entities, or objects, and notions, or conceptions. 2. Objectivity 
and objectuality. Truth and error. 3. Positive and negative (a) facts, 
(fo) notions, (c) convictions. 4. Schematic conceptions. 5. Categore- 
matic and syncategorematic words. 6. Subject and predicate. Substance 
and Accident, or Substantum and Ascriptum. 

1. Ax entity is anything whatever that does, or may, exist. 
Spaces, times, substances, powers, actions, changes, quantities, 
and relations, are so many kinds of entity. Whatever actually 
exists is a real entity ; and when a thing does not exist, but 
is merely conceived of as existing, we use similar language to 
that which we would employ if it existed, and say that it is 
a possible, or an imaginary, entity. In the strictest sense that 
only is an entity which really exists. The essence of entity, 
however, does not lie in its existence, but in its being that which 
exists, and which, therefore, also may be of this or that nature. 

The word "entity " is equivalent to the word " thing " in that 
wide sense according to which we speak of all beings, or exist- 
ences, whatever, as things. The advantage of the philosophi- 
cal term is that it has one signification only, while the word 
" thing " has many meanings. 

That action or state of intellect which corresponds to any 
entity is called a notion, or conception ; the entity of which 
we conceive is called the "object" of the conception, and the 
conception, as related to and corresponding with its object, 
may be said to be objective, or to have objectivity. 

This objectivity belongs to the essence of thought. Any 
psychical activity which does not correspond to things, or 
entities, is not thought, but some other form of experience. 
To this statement, however, the thoughts of existence and of 
non-existence, and they alone, present an exception. Existence 



32 THE MODALIST. [Chap. IV. 

and non-existence are not things, or objects, in the full sense 
of these terms, though they may be thought of just as things 
are thought of, and must be allowed (that is, in all cases of 
fact) to have a kind of objectuality. 

2. By " objectuality" we mean the character of things as 
being actually or possibly correspondent to our thought. The 
objectuality of entity is the counterpart of the objectivity of 
conception. But this objectivity of thought and this objectu- 
ality of things do not involve that a thought and the entity 
corresponding to it are of the same nature, or that they resem- 
ble one another, or that, if either exist, the other must exist 
also. They only imply that the nature of the oiie corresponds 
with the nature of the other. If the existence of a concep- 
tion always involved that of the corresponding entity, there 
could be no such things as truth and error. Truth lies in the 
conformity of thought with fact, or with what, in case some 
hypothesis were realized, would be fact ; while error is the 
disagreement, or want of correspondence, between thought 
and fact. 

3. Now fact is of two kinds or modes, — the positive and 
the negative. According to the first the existence of a thing- 
is a fact ; according to the second, the non-existence. It is as 
much a fact that there is no bread in the cupboard, when that 
is true, as that there is bread in the cupboard, when that is 
true. Consequently, and corresponding to the positive and 
negative modes of fact, there are two modes of conception, — 
the positive and the negative. 

These are expressed, respectively, by such terms as " bread," 
"a loaf," and "no bread," "no loaf." Commonly a thing is set 
forth as existing by a noun without the adjective " no," and as 
non-existent by the same noun with the word "no" prefixed. 
At first sight it appears self-contradictory to speak of a thing, 
or entity, as non-existent ; and it would be so if we intended 
to speak of a real entity as non-existent. But such is not the 
case. The only reality perceived and asserted is the fact of 
non-existence in a case where a certain entity may be imagined 
or supposed to be. Combining our conception of this entity, 
considered only as to its nature, with the thought of non-exist- 



Chap. IV.] ENTITIES AND CONCEPTIONS. 33 

ence, we exercise belief in connection with this combination. 
There is no incongruity in so doing. For we do not think of 
a thing as both existing and not existing at the same time ; 
we simply displace from the positive conception of a thing 
the elementary thought of existence, and replace this by the 
thought of non-existence. 

The distinction between positive and negative conceptions 
shows how we may exercise belief in connection with notions 
as well as in connection with propositions ; because belief is 
possible whenever our thought in any way contains the ele- 
ment either of existence or of non-existence. The forming and 
holding of conceptions as setting forth fact or truth is what 
logicians have had in mind in teaching that " simple apprehen- 
sion" is one of the three logical operations of the intellect. 
Whether Ave know something as a reality, or assume it to be 
such for the sake of argument, this apprehending and holding 
of a thing as true differs from the mere conceiving of a thing. 
It is even more than the conceiving of it as existing : it in- 
volves a real or affected belief in connection with our concep- 
tion. 

4. The division of notions, with reference to their fitness to 
correspond with realities, into the positive and the negative, is 
not an exhaustive division. There is a third class of concep- 
tions, — the formal, or schematic. For should we, in conceiving 
of any entity, think neither of its existence nor of its non- 
existence, but only of its nature or characteristics, we might 
express this by saying that we think of it merely as a form, or 
schema. According to this use of language a " form " includes 
everything in an entity except its existence. This mode of 
conception is difficult of deliberate realization ; but it occurs 
spontaneously sometimes, and especially whenever, after being 
ignorant about a thing, we learn whether it exists or not. For 
then, in our assertion respecting fact, we unite the thought of 
existence, or that of non-existence, with the schematic notion 
of the entity in question, and exercise belief in connection 
with this combination. 

In every pair of conceptions contrasted with each other as 
positive and negative there is a part common to both; that 



M THE MODALIST. [Chap. IV. 

part, when thought separately, is the formal, or schematic, 
conception. This mode of intellectual action has greatly 
escaped attention; it should have a place in every system of 
logic. 



.>. 



Another division of notions, less searching in its thought 



than the foregoing, distinguishes between the complete and 
the supplementary. A complete notion is one sufficient of 
itself to serve as a term — that is, as either subject or predi- 
cate — in a proposition ; but a supplementary notion can only 
help to constitute a term. In the sentence " The white flakes 
of snow are falling gently on the grass," the adjective, the 
participle, and the nouns express complete notions, while the 
articles, the prepositions, and the adverb express supplemen- 
tary notions. 

Words significant of complete conceptions were called by 
the old logicians " categorematic," from the Greek Kar-qyopr^ia, 
which signifies an assertion ; while words whose force is 
merely supplementary were styled syncategorematic. A term 
which contains only one complete notion or categorematic 
word is said to be simple, but when several complete notions 
are combined in one term, it is called complex. In the above 
illustration both terms, namely, " the white flakes of snow " 
and " falling gently on the grass," are complex. 

The distinction between complete and supplementary con- 
ceptions, and between categorematic and syncategorematic 
words, arises rather from our mode of employing ideas than 
from the essential nature of our thought ; for direct and atten- 
tive thinking can give an independence to any conception 
whatever, and fit it for categorematic use. But this distinc- 
tion prepares us to determine at once whether a proposition be 
fully formed or not, and what its terms may be. A thorough 
analysis of the component thoughts out of which terms or com- 
plete notions are constructed belongs to metaphysical psychol- 
ogy. Commonly in logic when we speak of conceptions we 
refer to complete conceptions. 

6. This is especially the case in that division which distin- 
guishes between subjective and predicative notions ; for only a 
complete notion can be either subject or predicate. 



Chap. IV.] ENTITIES AND CONCEPTIONS. 35 

Ordinarily, in making an assertion, we think of one thing, or 
entity, as existing, and then present another thing, either as 
existing, or as not existing, in some relation to the first. In 
saying "the snow is white," "the snow is not yellow," we 
think of snow as existing, and then assert that the quality 
indicated by "white" exists in the, snow, and that the quality 
indicated by "yellow" does not exist in it. The first entity 
thought of in the assertion is called the subject, and the second 
the predicate ; which terms are also applied to the correspond- 
ing conceptions. In common language, the subject is that 
about which some assertion is made, while the predicate shows 
what is asserted about it. Obviously, the meaning which 
logic thus attaches to the term "'subject," is very different 
from that belonging to it in psychology, and according to 
which it signifies a thinking and sentient spirit. 

The terms "subject" and "predicate" are applied, not only 
to things thought of in assertions, and to our conceptions of 
those things, but also to the words expressive of the concep- 
tions. In the sentence, " The rose is red," the words " rose " 
and "red" are subject and predicate. But whatever maybe 
the immediate application of these terms, they always refer- 
to that use which we make of our conceptions when we affirm 
or deny one thing of another. 

Two things which can be thought of as subject and predi- 
cate, and so as related to the faculty of judgment, may also be 
thought of simply as related to each other, and without refer- 
ence to our assertion about them. In that light they have 
been named substance and accident, these designations being 
thus employed in a very peculiar way. 

In logic, any entity whatever of which we conceive indepen- 
dently and about which we can make assertions — that is, any- 
thing whatever, as existing in predicable relations — is called 
a substance. In metaphysics we say that there are two kinds 
of substance, spirit and matter; in logic, spaces and times, 
powers and actions, changes, qualities, and relations are sub- 
stances. When we speak of " the height of the column," " the 
beauty of the picture," " the wisdom of the judge," the height, 
the beauty, and the wisdom are logical substances, no less 



oG THE MODALIST. [Chap. IV. 

than the column, the picture, and the judge ; for they may be 
subjects of predication. 

In some discussions a distinctive name for the logical sub- 
stance would prove advantageous ; therefore we may occasion- 
ally speak of it as a substantum. 

The term "accident," also, has a different meaning in this 
connection from what it has elsewhere, even in logic. For it 
is applicable to any predicate entity ivhatever as united in being 
to a subject entity. According to this sense the necessary prop- 
erties of a thing, and even its essential attributes, are acci- 
dents. It would be well if some other word could be found to 
express this very general idea. Possibly the term " ascript," 
or " ascriphim" would serve the purpose. Then, when think- 
ing objectively, the logician might speak of "substanta" and 
" ascripta " ; though more frequently, and because he con- 
stantly considers the relation of tilings to thought, he will 
speak of "subjects" and "predicates." 



Chap. V.] GENERAL AND INDIVIDUAL NOTIONS. 37 



CHAPTER V. 

GENERAL AND INDIVIDUAL NOTIONS. 

1. General notions. 2. The process of generalization. 3. The expres- 
sion of general conceptions. 4. Realism, Nominalism, and Conceptualising 
4> Universals." 5. Individual, or numerical, difference. Specific difference. 
6. Identity, numerical and specific. 7. The " principium individuationis." 
8. "Individual" notions include (a) the singular, (6) the definite, (c) the. 
indefinite, (d) the class notion ; and are either unital or plural. 9. "All," 
distributively and collectively. 10. A restricted application of the term 
' ' individual. ' ' 

1. Ax important logical distinction divides notions into the 
individual and the general. A notion is general when it is 
applicable to any of a class of similars simply on account of 
their similarity, and when it does not include the thought 
either of one object or of more than one. In saying "man is 
mortal " we do not conceive either of one man or of more than 
one, but only think that general notion, "man," which is 
applicable either to one man or to many. Should we say, " a 
man is mortal," or " any man is mortal," the words " a man " 
or "any man" would express, not a general, but an indefinite 
individual notion; which, however, is closely allied to the 
general. 

2. Every general conception originates in a process called 
" generalization " ; and this may be described as consisting of 
two steps, or stages. First, by an act of abstract thinking, we 
consider a number of objects so far as they are alike, with- 
drawing our thought from those respects in which they are 
unlike. This act is often preceded by a comparison of the 
objects, that is, by that process in which things are contem- 
plated together for the purpose of perceiving their points of 
similarity and dissimilarity. This comparison is not always 
needed, and is easily distinguished from that act of abstraction 
in which the work of generalization properly begins. 



38 THE MODAL 1ST. [Chap. V. 

The second step is the more essential one. In it, taking one 
or more of the objects as a sample or samples of the class of 
similars, we drop from oar conception all thought of individual 
difference — all thought of number, whether of one or more 
than one ; the conception which remains is a general notion. 
Thus, having perceived the similarity between many pieces of 
gold, we easily think of those many pieces nnder one plural 
conception, or we consider one piece as a sample of all ; then, 
rejecting the element of individuality, we think and speak of 
" gold " in the general. 

Some say that, in generalization, we conceive of " the many 
as the one " and of " the similar as the same." This language 
is incorrect and misleading. In generalization we do not 
regard a number of different things as if they were one and 
the same, but we discard all reference either to diversity and 
similarity or to unity and plurality, and then think that one 
thought ivhich remains. 

3. General notions, conceived independently, are expressed 
by common nouns, either without any addition or with the 
definite article prefixed. We say either " man/' " gold," " wis- 
dom," or "the pulpit," "the press," "the theatre." This use 
of the article indicates that the conception belongs to a class 
of objects well-known, and perhaps known in contrast with 
other classes somewhat resembling it, and, in so doing, it 
makes an addition to the general notion. For instance, "the 
pulpit," "the press," and "the theatre" are general designa- 
tions applicable to well-known agencies of instruction, which 
also may be compared with one another. Since it is always 
possible to conceive, in this distinctive way, of things in the 
general, a choice is given between the simpler and the more 
precise form of expression. Some languages prefer the one ; 
others the other. 

The above-mentioned modes of conveying general notions 
by the nse of nouns are the direct and proper methods. Other 
ways are employed, of which we shall speak presently, and 
which may be characterized as indirect and improper. 

4. In using general thought and language we seem to be 
speaking about things, and we say that we are speaking about 



Chap. V.] GEN Eli AL AND INDIVIDUAL NOTIONS. 39 



things. This fact is the chief foundation for a doctrine, once 
very prevalent, that there are real entities corresponding to 



■•eneral notions as such. These entities were called " univer- 
sals," and were considered eternal patterns, which, in some 
way, prepared for, and contributed to, the existence of indi- 
vidual entities. Thus it was held that man and tree and life 
and death and virtue and vice are universals, and that each of 
these imparts its nature to a large class of individuals as they 
come into being. The advocates of this doctrine were styled 
Realists, because they asserted the reality of general objects; 
they were opposed by the Nominalists, who taught that there 
are no such things even as general conceptions, and that uni- 
versality belongs only to those names, or words, which may be 
applied to all the members of a class. A third doctrine, avoid- 
ing the extremes both of Nominalism and of Realism, has been 
called Conceptualism, because, while denying the reality of 
universals, it maintains that mankind constantly form and use 
general ideas. These ideas are not in their own nature general 
entities, but individual mental states. They are styled gen- 
eral because they are applicable to every member of a genus, 
or kind; for which reason they are also sometimes spoken 
of as universal notions. 

The prevalence of Realism in former times and its influence, 
even at the present day, have been greatly promoted by the 
preference of man's mind for positive thinking and belief ; we 
are naturally prone to believe that there are objects corre- 
sponding to our conceptions. This tendency favors Idealism, 
or the theory that the objects of the imagination really exist, 
as well as Realism. Language, too, falls in with both these 
delusions ; for the very same words sometimes express actual- 
istic conviction and refer to real objects, and sometimes 
express merely modes of thinking — imaginative or rational. 
Moreover, the fact that general conceptions and language are 
being continually apjilied to existing individuals with little 
notice on our part of any change in the method of our thought 
lends further aid to Realism. For the validity, or truthful- 
ness, of general statements lies wholly in their applicability. 

5. Let us now turn to individual conceptions. These are 



40 THE MOBALIST. [Chap. V. 

distinguished from general conceptions because they are always 
modified, by the thought of number, whereas a general notion 
excludes the qualification either of oneness or of plurality. 
An individual notion, such as "a dollar" or "dollars," always 
stands for what is, or may be, in strict literality, one thing or 
a number of things. 

Every such entity is called an individual because it does 
not admit of "logical division." The general notion "dollar," 
as representing a class of things, may be divided into "gold 
dollar," "silver dollar," and "paper dollar"; and, in like 
manner, every genus may be divided into its species. But an 
individual dollar cannot be separated, even in thought, into a 
number of dollars, or things having the same general nature 
with itself. When, in the descending process of division, we 
come to the individual, we can go no farther. 

The thought of individuality, like those of existence, non- 
existence, and entity, is simple and incapable of analytical 
definition. It is nearly identical with arithmetical " oneness " 
or " unity " ; though oneness, in addition to individuality, in- 
cludes the characteristic of quantity, and so sets forth every 
individual as a distinguishable quantum of entity. 

When, along with a first one, another unit presents itself, 
we immediately perceive the relation of " otherness " existing 
between them, and so, considering them as quanta, we say that 
there are two individuals. All conceptions of number start 
from this beginning ; hence the relation of otherness has been 
named numerical difference. Then, by a natural metonymy, 
that characteristic in every entity which is the basis of this 
otherness, is also called "difference." In other words, indi- 
viduality, as the ground of otherness, is styled "numerical 
difference." So every individual may be said not only to be 
numerically different from every other, but also to have 
numerical difference in itself. 

This difference is easily distinguished from that which 
exists between objects as being unlike each other. The latter 
is often called " diversity " ; and it is also styled " specific 
difference," because it is the ground of dividing entities into 
species, or kinds. Two rain-drops might be so absolutely 



Chap. V.] GENERAL AND INDIVIDUAL NOTIONS. 41 

alike that they would differ only , numerically ; but there is 
specific as well as numerical difference between a rain-drop 
and a pebble. 

6. Individual, or numerical, identity is that absence, or non- 
existence, of numerical difference which is perceived when any 
entity thought of once is compared with itself thought of again ; 
it is a necessary attribute of every individual entity ; it is what 
we mean by " sameness " in the strictest sense of the word. 

Specific identity, on the other hand, is merely the perfect 
similarity which exists between two or more entities so far as 
they are members of the same species or genus ; it is the 
" sameness " mentioned when we say that a thing may be done 
twice in the same way, or that all quadrupeds have the same 
bodily structure. 

7. In scholastic times there was great discussion as to the 
"principiuni individuationis," or origin of individuality. The 
Kealists held that individuals result from the conjunction 
of " universal " forms with the otherwise " undifferentiated 
matter " of being. But such forms and such matter are merely 
philosophical imaginations. The truth is that everything 
which exists has both individuality and definiteness in every 
part of its nature ; these attributes begin and cease to exist 
as necessary elements of the entity itself. 

8. Notions are styled individual because of the individuality 
of the things corresponding to them, and this equally whether 
a notion represents one thing or more than one. Hence in 
common language we might say that individual notions may 
be either singular or plural, but in logic we must say that this 
class of conceptions may be either unital or plural. For the 
term " singular," as we shall soon see, has a signification in 
logic quite different from that given to it in grammar, and 
therefore ought not to be used in logic in its grammatical 
sense. Such expressions as "a man," "men," "some men.'' 
"any man," "all men," "this man," "that man," "these men." 
"those men," "the man," "the men," " George," "the Georges," 
"President Cleveland," "his predecessors," "the presidents 
of the United States," represent individuals, and therefore set 
forth individual notions. 



42 THE MODALIST. [Chap. V. 

But while ail miital and all plural conceptions are individual, 
and, under this title, are contrasted with general notions, the 
term " individual " is also employed sometimes in a more 
restricted application, as will be better understood after we 
consider four kinds, or classes, into which individual notions 
may be divided. 

The first of these comprises those conceptions which logi- 
cians characterize as singular, and in which we conceive of an 
object as having marks peculiar to it, or of more than one 
object as having marks peculiar to them severally. For such 
ideas are unique, or singular, in their composition. These 
thoughts are often expressed by proper names, as when we 
speak of Niagara, the St. Lawrence, Washington, Caesar, Lon- 
don, Paris ; but they are also indicated by the common noun 
with the definite article or a demonstrative pronoun, it being 
then understood that the objects are known by means of marks 
peculiar to each of them, and not merely by some general char- 
acter. If, in conversation respecting given persons or places, 
one should say, "I admire that man greatly," "I hope to visit 
those cities," the words, " that man," " those cities," would 
represent singular conceptions. 

This same mode of speech, however, would express another 
class of notions if the objects mentioned were conceived of as 
definitely related individuals of a certain kind, yet without 
thought of peculiarities belonging to each of them. One 
might speak of "the President who was lately inaugurated," 
or of "the lawyer who has the case in charge," thinking of 
each only in his character as president or as lawyer, and con- 
veying only this conception to others. Such ideas, because 
presenting objects as singularly related, though not as having 
peculiar natures, might be regarded as imperfectly singular. 
But they have been called "definite" individual notions, and, 
under this name, have been distinguished from singular no- 
tions ; that is, from those perfectly and internally singularized. 

A third species of notions to be mentioned here are the 
indefinite individual, or, more simply, the indefinite. Por we 
may form a thought of a member of a class, or of more mem- 
bers than one, without determining our conception to any par- 



Chap. V.] GENERAL AND INDIVIDUAL NOTIONS. 43 

ticular member or members. Such notions are indicated by 
the indefinite article and by the adjectives "any," "some," 
"several," "many," and other expressions of like meaning. 

These conceptions, in themselves, are only the result of an 
indeterminate kind of thinking ; but they are often used as 
substitutes for general conceptions. For example, the state- 
ment " a man — or any man — is mortal " may replace " man 
is mortal," because what is true of any man, taken at random, 
may be said of man in general. In like manner, the state- 
ment, " Some men live to a great age," may serve instead of 
" Man may live to a great age," because the probability, or 
contingency, in regard to man in general arises from the fact 
known indeterminately regarding some. 

The fourth and last kind of individual conception is the 
class notion ; and this, like the others, may be either unital or 
plural. The unital class notion is indicated by the adjective 
" every " ; the plural, by " all." The word " every " empha- 
sizes the individuality of the things mentioned; the word 
" all," the universality of the statement about them : thus 
only we distinguish " every man must die " from " all men 
must die." In each case both individuality and universality 
are included in our thought. 

9. For this reason it is important to notice a use of the 
adjective "all," which does not present the members of a 
class in their independent individuality, and therefore does 
not express a class notion. In saying "All the soldiers are 
brave men," we employ the word " all " distributively, as the 
logicians say, and consider the soldiers in their independent 
individuality. But should we say, " All the soldiers are the 
king's army," we would use "all" collectively, and would con- 
sider the soldiers, not merely as so many individuals, but as 
being united together ; for it is only as united that they are 
an army. The Latin language provides for these two senses 
of the adjective by the terms "omnes" and "cuncti," this last 
being a contraction of "conjuncti." Whenever the subject of 
a proposition is a class notion, it must always be understood 
distributively, because a class considered collectively is no 
longer, for the purposes of logic, a class, but only an individ- 



44 THE MODALIST. [Chap. V. 

ual resulting from the union of individuals. "All men," as 
the family of Adam, or as the human race, are an individual, 
just as a congregation, a crew, a library, or a vocabulary is an 
individual. 

The class notion is often used instead of the general notion 
when we wish to assert something as necessarily, and there- 
fore universally, true respecting things of a given nature. 
When we say, "Every man is fallible," "All men are mortal," 
we give the form of individuality to the general truths that 
"man may be deceived," and that "man must die." The 
individualized assertion is an immediate consequence of the 
general truth, and has the advantage of being more closely 
related to actuality. 

10. Having defined the four kinds of individual notions, we 
can now explain, in few words, that restricted application in 
which the term "individual" is sometimes used. It is that 
which contrasts the individual with the singular, and which 
therefore includes under the individual only the definite, the 
indefinite, and the class notions. For in all these we think of 
objects simply as individuals possessing a common nature. 
In this restricted sense individual conceptions are opposed to 
both singular and general conceptions. 



Chap. VI.] PREDICATIVE NOTIONS. 45 



CHAPTER VI. 

PREDICATIVE NOTIONS. 

"The Ten Categories." 

1. Subjective notions set forth, substanta. Are of primary and of 
secondary conception. 2. Improperly distinguished as "concrete and 
abstract." 3. The ten categories of predication. 4. Substance as predi- 
cate. 5. Quantity. 6. Quality. 7. Relation. 8. Place, time, posture, 
condition, action, passion. 9. The substantialization of ascripts. 

The chief logical significance of conceptions arises from the 
employment of them as the subjects and predicates of propo- 
sitions, but especially from their use as predicates. This 
involves many important modifications of thought. 

1. All subjective notions set forth a " substantum," or logi- 
cal substance ; and their nature as substantal conceptions will 
be sufficiently illustrated if we divide them into those of 
primary and those of secondary conception ; or, more simply, 
into the primary and the secondary. For while everything, 
of whatever kind, may be conceived of as a logical substance 
and as a subject of predication, some forms of entity are 
thought of in this way at once, while others are first conceived 
of ascriptionally, or predicationally, and only afterwards are 
treated as substanta. For instance, we think primarily of 
bodies and spirits — that is, of substances in the metaphysical 
sense — as substanta, and of the powers inherent in those 
substances as qualities to be predicated of them. Hence we 
say, "The scholar is wise," "The horse is strong." In like 
manner we conceive of a space as a substantum and of its size 
as an ascriptum, and say, " The room is large." Often, however, 
after some form of entity has been conceived of in the ascrip- 
tional way, we are led to think of it independently, and find 
ourselves doing so even while retaining in our minds a refer- 



46 THE MOBALIST. [Chap. VI. 

ence to our primary mode of thinking. In this way subjective 
notions of secondary conception arise. Thus from the predi- 
cates, or ascripta, in the cases given above, we may form the 
substantal notions " wisdom," " strength," and " largeness," or 
"magnitude." 

2. The foregoing distinction is commonly expressed by the 
division of nouns, or of substantal notions, into the " concrete" 
and the "abstract." But these terms, though they indicate 
a difference, throw little light upon its nature. For the so- 
called "concrete" notion, if it be a general one — as "man," 
"animal," "matter," "spirit" — is formed by abstraction ; and 
the so-called "abstract" notion, if it be complicated, involves 
a synthesis, or concretion, of ideas. For example, by synthesis 
we conceive of guiltiness as " a liability to penalty because of 
an infraction of moral law." Therefore, in a very natural 
sense, substantal notions of primary conception may be ab- 
stract, and those of secondary conception, concrete. This 
infelicity, arising from a conventional application of terms, 
illustrates a difficulty, which cannot always be avoided, in the 
expression of philosophical truth. 

3. We now turn to the discussion of predicative notions. 
The earliest classification of these is one given by Aristotle. 

He says, "The Categories are ten in number, what a thing 
is (ovata), quantity (iroaov), quality (ttoZov), relation (?rpos 
t/), Avhere (ttov), when (-ttotc), position (kuo-Ooll), possession 
(eXeiv), passion (7rao-xeiv), action (7rotav)." The term Kar-qyopia 
originally meant an assertion, but here signifies a generic 
class, or summum genus, of things assertible. For, as Aris- 
totle says, " Every proposition sets forth either ' what a thing 
is ' or some other category." 

This enumeration of predicative notions cannot be rejected 
as incorrect, yet is not closely connected with the laws of con- 
viction. It belongs to a primary stage of logical theory, and 
is chiefly valuable as bringing before us, for further considera- 
tion, every form of ascriptional thought. 

4. The first category, "what a thing is," was also named by 
Aristotle oiWa, which term the scholastics translated by " sub- 
stantia," or substance. The teachings of logicians regarding 



Chap. VI.] PREDICATIVE NOTIONS. 47 

this substance are confusing in the extreme, but we will arrive 
at its true nature if we remember that it is the form of predi- 
cation expressed by a noun — that is, by the " noun substan- 
tive," as this was formerly distinguished by grammarians 
from the "noun adjective." In saying, "The man is a mer- 
chant," "'Honesty is a virtue," the substance "merchant" is 
predicated of man, and the substance "virtue" of honesty. 
But while the term " substance " here clearly means a sub- 
stantum, or logical substance, we cannot but observe that the 
application of it to the predicate of a proposition is accom- 
panied by a modification of meaning. The subject of a propo- 
sition must always be conceived of independently before we 
can rightly say anything about it; therefore whatever is fit 
to be the subject of an assertion is a substantum in the full 
sense of the word. But no such independence of conception 
belongs to any predicative thought. The first of the ten cate- 
gories may appear to have it, because this category originates 
in substantal conception, and is expressed by a noun. But a 
noun used predicatively is preceded by a mental addition which 
destroys the independence of its conception. For it then sets 
forth the predicate-substantum either as identical, or as not 
identical, with the subject-substantum ; and this is quite a dif- 
ferent thing from setting forth a substantum simply. 

When we say that "the man is a thief," or that "the man 
is not a thief," we assert that the man is, or that he is not, 
identical (numerically) with a thief; we do not say merely 
that the man exists, and that the thief exists. Locke, and 
Leibnitz after him, perceived this mental addition, and hence, 
in their writings, the category of substance gives place to that 
of " identity and difference." There is, however, some advan- 
tage in retaining the old name. For the work of this form of 
predication is not completed in the assertion of identity or 
difference. Were that so, the category of " substance " would 
be only a specific form of the category of "relation." The j 
true end of the predication of substance is to convey the infor- 
mation that a subject, already known as having one nature or 
aspect, has, or has not, another also. The statement, "The 
man is a thief," asserts that a subject known as a human 



-V 



48 THE MODALIST. [Chap. VI. 

being has the character of a thief; the corresponding negative 
statement denies that he has that character. In short, numer- 
ical identity or difference is here used to set forth the exist- 
ence, or the non-existence, of a nature, or character, as belong- 
ing to a subject. Aristotle indicates this when he says that 
the first category shows "what a thing is," and in the name 
ovaia ; for ova-La primarily signifies nature, or essence. 

The secondary application of the term " substance " or " sub- 
stantum," which we have now considered, gives rise to a 
secondary use of the corresponding term " ascript " or " ascrip- 
tum." Strictly and primarily every category of predication is 
an ascriptum, and, under this name, is contrasted with the 
substantum, or subject, to which it belongs. But when, in 
the classification and discussion of predications, we find one 
category called " substance," we naturally restrict the term 
" ascript " to the remaining categories, and thereupon we divide 
predicate notions into two comprehensive classes, the substantal 
and the ascriptional. Such language is scarcely avoidable when 
one may be speaking concerning the different kinds of predi- 
cation, but it need not produce confusion, if we exercise care. 

5. The second category — quantity — is used in asserting 
that something exists in a given degree or amount. In say- 
ing, "The road is ten miles long; the house is one hundred 
years old," we ascribe a definite age to the house and a definite 
length to the road ; referring in each case to an appropriate 
unit of measure. And even in saying, " The house is old ; the- 
road is long," there is a tacit comparison with some standard. 
It is only this measured quantity that calls for a specific cate- 
gory. Quantity, simply as quantity, belongs to and character- 
izes every form of entity. It might be regarded as a kind of 
universal quality. As it may always be assumed, the predica- 
tion of quantity, simply as quantity, seldom takes place. 

6. The category of quality sets forth whatever does or may 
permanently mark an entity, and so be the ground of its clas- 
sification with other entities similarly marked. This category 
is primarily expressed by the adjective, as when we say, "The 
man is wise; the table is round; the business is urgent." 
Ordinarily and properly the characterizing entity is attached 



Ciiaf. VI.] PREDICATIVE NOTIONS. 49 

to the subject permanently ; yet this condition may be dis- 
pensed with, provided only the mark be permanently con- 
nected with the subject in our conception. A dethroned king 
may still be thought of as a royal person ; the general who has 
concluded a war successfully may be regarded for life as a vic- 
torious commander. In fact, the category of quality, like that 
of substance, is all-embracing in its power to use material ; for 
any mode or combination of entity may be so used as to char- 
acterize the subject to which it is related. 

7. The fourth category assumes that there are two or more 
entities, and then simply asserts (or denies) the existence of 
a relation between them. Thus setting forth the relation 
of cause and effect, we say, indifferently, "Fire is the cause of 
heat," or, "Heat is the effect of fire." The linguistic form 
of these statements belongs to the category of substance, yet 
they do not predicate substance, because their aim is simply to 
assert relation, and not nature, or kind. We may also express 
relation by saying, "Fire produces heat, or is productive of 
heat," provided our intention is not to assert that heat is 
being produced, or that fire can produce it, but the fact that 
heat is produced by fire. Eelations are primarily expressed 
by prepositions, but are often set forth in this secondary way 
by nouns, or verbs, or adjectives. 

In speaking of relations as existing betiveen entities, our lan- 
guage is based on the circumstance that the conception of a 
relation comes intermediately between those of the relata. 
In strict truth, however, a relation is not an intermediate 
entity, but is composed of two parts, or relationships, one of 
which resides in each of the things related. This doubleness, 
or plurality, appears in the relation of husband and wife, of 
agent and instrument, of cause and effect, of equals, of un- 
equals, of the container and the contained, and in all other 
relations. 

8. The next category is that of place. Some have objected 
to this category that it is merely a specific mode of the cate- 
gory of relation. But it is, or at least may be, more than this. 
"The king lives in a marble palace," sets forth both that there 
is a marble palace and that the king lives in it. In like man- 



50 THE MODALIST. [Chap. VI 

ner, a relation and something more are expressed by the cate- 
gory of "time." "The marriage took place last Thursday/' 
indicates both that an event occurred at a certain date, and 
that a certain time has elapsed since that date. 

The categories of "position" and "possession" might better 
be named "posture" and "condition." They also have a 
doubleness. To say, " John sits," or, " John is resolved," sets 
forth a posture of body or of mind in which the parts of 
the body or the thoughts of the mind are adjusted to each 
other, and are, moreover, externally related. For one sits on 
some seat, and is resolved on some conduct. In the same way 
the sentence, "John is well, and John is wealthy," indicates 
first the existence of health and wealth, and then the con- 
dition in which John finds himself as the possessor of these 
blessings. 

Finally, the categories of "action" and "passion" both set 
forth the operation of some power, but the one in relation to 
the agent or instrument, the other in relation to the thing 
acted upon. Therefore these, also, are duplex. 

9. Having familiarized ourselves with the natural forms of 
predicative thought, as presented in the "ten categories," and 
having seen that predicative conceptions may be divided into 
two general classes, the substantal and the ascriptional, we 
must not fail to note, in conclusion, an important point. This 
is that either the substantal or the ascriptional mode of predi- 
cative conception may take the place of the other. Especially 
we must understand how a statement with an ascriptional 
predicate may, by a slight addition, be changed into an 
equivalent statement with a substantal predicate ; for a change 
of this kind often takes place necessarily in the course of our 
reasonings. When we say, " Some men are wise ; therefore 
some wise beings are men," this reasoning is valid only because 
we replace the ascriptional proposition, " Some men are wise," 
by the substantal proposition, " Some men are wise beings." 
So, in the syllogism " Man is rational ; every rational being 
is accountable; therefore man is an accountable being," the 
argument would not be conclusive if it were not lawful to 
replace the ascriptional term, "rational," by the substantal 



Chap. VI. ] PREDICATIVE NOTIONS. 51 

term, " rational being." Moreover, in the final proposition of 
this syllogism we have found ourselves at liberty to adopt the 
substantal form of assertion, though the ascriptional form 
might have been retained. 

The thought of the " being," or " entity," which is added in 
these modifications of conceptions is that of the substantum to 
which the ascript belongs. We have the right to make this 
addition, because, when any subject has an ascriptional predi- 
cate, it may, of course, be identified with itself as a substantum 
having that ascript, and, when it has not a given ascript, we 
can say that it is not a substantum which has it. 

This process might be called the substantialization ofascripts. 

The reverse process, of de-substantialization, consists in 
dropping the thought of substance. Instead of saying, " Man 
is a mortal," we say, " Man is mortal." This change occurs 
frequently, but is of less logical consequence than the other. 



52 THE MODALIST. [Chap. VII. 



CHAPTER VII. 

PREDICATIVE NOTIONS. 

"The Five Predicables." 

1. Defined and enumerated. 2. Genus and species here signify natures, 
not classes. 3. Species, essence, definition, and nature, distinguished. 

4. Difference, as a predicate, is not the relation, but the ground of it. 

5. Property. Generic and specific. Often becomes attribute. 6. Accident. 
Here opposed to essence and property, not to substance or subject or 
being. Separable as regards the nature ; separable or inseparable as 
regards the object. 7. The " predicables ' ' are used only when logical 
connection is conceived exactly. 8. Attributes. Adjuncts. Qualities. 

1. A second division of predicative notions given by Aris- 
totle is known as " the five predicables." This classifies all the 
possible predicates of any subject, not with reference to their 
own differences, as in the categories, but according to their exact 
connection with the nature of the subject. The distinctions thus 
presented are quite important ; because the force of a proposi- 
tion, either as setting forth truth or as a premise in argument, 
varies with the mode in which the predicate is logically 
related to the subject, or, as Aristotle would say, with the 
mode of the inherency of the predicate in the subject. 

Logicians formerly taught that every predication used in 
reasoning not only conforms to one of the. ten categories, but 
also to one of the five ■ predicables — in other words, that it 
not only asserts substance, quantity, quality, relation, or 
something else, of a subject, but also presents the predicate, 
employed as related to the nature of the subject in one or 
other of five ways. They expressed this by saying that every 
proposition sets forth either the genus, th-e species, the differ- 
ence, the property, or the accident, of a thing ; and they held 
that all reasoning arises in connection with these last-men- 



Chap. VII. ] PREDICATIVE NOTIONS. 53 

tioned modes of apprehension; which, therefore, by way of 
pre-eminence, were called the predicables. These views are 
extreme. Predications, and reasonings by means of them, 
may take place without reference to any predicable. But it is 
true that these modifications of assertive thought are often 
employed in our more thorough thinkings, and that they have 
an important function in the apprehension and statement of 
truth. 

2. The first predicable is genus (yeVos). This term frequently 
signifies a class of similars in which other classes of similars, 
differing from one another, are comprehended. According to 
this sense the genus, " forest-tree," comprehends oaks, beeches, 
maples, elms, and so on. In the present connection genus 
means, not the generic class, but that nature which belongs to 
every member of it. When we say that the oak is a forest- 
tree, and think of it as having the nature of all forest-trees, 
and distinguish this nature from the peculiarities of the oak, 
we predicate genus of it. 

Since it is part, though not all, of our conception of the 
nature of the oak that it is a forest-tree, the predication of 
genus does not, in this case, add to our knowledge of what an 
oak is, but only makes a part of our knowledge explicit. If, 
however, we were ignorant concerning the nature of an oak, 
or of anything else, the predication of genus would enlarge 
our information, and would not be merely explicative of a con- 
ception already entertained. The predication of " species " or 
of " difference " may, also, be employed in either of these 
ways. 

The question may be asked, " Is the nature asserted in the 
predication of genus individual or general ? " We reply that 
it is either, according to the character of the subject. The 
predicate of a general subject is necessarily general, and that 
of an individual subject individual. Should we speak in gen- 
eral and say, " The oak is a deciduous tree," all our thought 
would be general ; a similar assertion made about this or that 
oak would be individualized throughout. We do, indeed, say 
that the individual tree has a generic nature, but this use of 
language is secondary and metonymical. It does not mean 



54 THE MODALIST. [Chap. VII. 

that the tree has literally a generic nature, or a general 
nature of any description, but only that part of the individual 
nature corresponds to a generic conception. 

The second predicable is designated "species" (eF8o?). This 
term often signifies a subordinate class of similars, but, in the 
present connection, it means the nature which characterizes 
such a class. We say that, while man is, according to genus, 
an animal, he is, according to species, the rational animal. 
Thus it appears that " species " comprehends " genus " together 
with a " difference," by which the given species is distinguished 
from other species of the same general kind. 

3. The predication of species, however, is not the mere 
assertion that a subject has a certain distinctive nature united 
with a generic nature. It implies that the nature predicated 
{the species) is the ivhole nature which the subject has in common 
with other entities, so far as that nature may be conceived of by 
us. It would not give the species of horse to say that the 
horse is a quadrupedal mammal. This would only present a 
genus, though it would be a subordinate genus formed by the 
union of the higher nature " mammal " with the peculiarities 
of the specific nature " quadruped." To give the species, we 
must add those particulars regarding form and motion, parts 
and uses, which complete the conception "horse," as enter- 
tained by us. 

It is not, indeed, necessary for the purposes of definite and 
conclusive thinking that we should give all the particulars 
that enter into this conception. Very often one or two or 
three of the distinguishing features are sufficient, as repre- 
sentatives of all the specific peculiarities ; nevertheless it 
remains true that the predication of species is the predication 
of the whole nature conceived of. 

This was taught by Aristotle when he said that to give the 
species is to give the definition of a thing ; and it is involved 
in the doctrine that " species " and " essence " are identical, or 
nearly so. The predication of species and that of essence pre- 
sent exactly the same truth ; they differ only in that the former 
4. directs the mind to the substantal form of conception, while 
the latter dwells on the attributal, or qualitative. To say that 



Chap. VII.] PREDICATIVE NOTIONS. 55 

man is the rational animal (giving this predicate its full sub- 
stantal force) asserts species ; to say that man is rational and 
animal, or that he has a rational and an animal nature, gives 
his essence. Either form of statement, however, may be said 
to set forth either essence or species. 

Let us note here that, in logic, the term " nature " is closely 
related to "essence," and has precisely the same meaning 
whenever we refer to the whole nature, or constitution, of a 
subject. But we may speak of a generic nature, as when we 
say that the oak in its generic nature is a forest-tree ; while 
we do not speak of a generic essence. A nature, therefore, 
may be only part of an essence. 

4. The third predicable, "difference," has been designated 
also "specific difference," and is thus opposed to "numerical 
difference." Its office is to present, not the relation of differ- 
ence between different species, but the foundation of this rela- 
tion; namely, that peculiarity, or collection of peculiarities, 
which belongs to a species and distinguishes it from others in 
the same genus. Among plane figures bounded by curved 
lines the "difference" of a circle is that every part of the 
circumference is equally distant from a point within ; and the 
" difference " of man among animals is "rationality." 

Aristotle says that genus and difference are interchangeable 
and identical. In a certain sense this is true. We may think 
first of the genus " animal," and then of the difference 
" rational," which distinguishes one species of animal ; or we 
may think first of the genus " rational," and then of the dif- 
ference "animal," which distinguishes one kind of rational 
beings. In like manner, a circle and a sphere have the generic 
character that in each every part of the boundary is equally 
distant from a point within, the differences of these figures 
being that the one is solid and the other plane ; but, were 
circle compared with square, or sphere with cube, in either 
case, the genus given above would become difference and the 
difference genus. 

Nevertheless, though what is now genus may become differ- 
ence, and what is now difference may become genus, genus and 
difference are not the same ; nor is the predication of the one 



56 THE MOBALIST. [Chap. VII. 

*}- the predication of the other. A nature is genus as the founda- 
tion of resemblance between species ; it is difference as the 
foundation of diversity ; so that the same nature cannot be 
both genus and difference in reference to the same two specific 
classes. Genus and difference as such are not interchangeable 
with each other, but they may exist together for the same 
reason that two men, who are related as creditor and debtor, 
may, in their relations severally to two other men, be debtor 
and creditor. 

The " specific difference," now under consideration, is easily 
distinguished from that " individual difference " which belongs 
to entities simply as such, and whether they differ in nature 
or not. Moreover, when two individuals, being of different 
kinds, are said each to have its specific difference, this differ- 
ence is a part of the individual and is itself an individual 
thing. Yet it is not, on this account, what we call "individual" 
(or numerical) difference. To assert this latter is merely to 
say that one thing is not another ; but to assert the former is 
to say that one thing is unlike another. 

5. The fourth predicable is named "property," this term 
being thus used in a strict and technical sense. A property 
is that which is not included in an essence, or species, but 
which yet is necessarily, and therefore universally, connected 
with it. Thus it is the property of man to be a religious 
being, and of a plane triangle to have its three angles equal 
to two right angles. 

Property being inseparable from essence, our conception of 
an essence may easily be enlarged by incorporating with it 
that of some property ; upon which addition property ceases 
to be property and becomes attribute — that is, an essential 
characteristic. For this reason, and because our conceptions 
frequently vary in comprehensiveness, it may sometimes be 
difficult to say whether some necessary ascript be a property 
or an attribute. For example, since every quadrilateral figure 
is quadrangular too, one might ask, "Is it a part of the 
essence, or only a property, of such a figure to have four 
angles ? " The answer is that this is either a property or an 
attribute, according to the manner of our conception. Mostly, 



Chap. VII.] PREDICATIVE NOTIONS. 57 

for the sake of simplicity, the mind selects just so many lead- 
ing and permanent marks as are sufficient to distinguish a 
class of beings from all others, and excludes all remaining 
ascripts from its idea of essence. This is especially the case 
in the forming of definitions. Yet it is not invariably so. In 
conceiving of a triangle we think of three angles as well as 
of three sides, and recognize the angles as entering into the 
essence of a triangle, though they are inseparably involved 
with the sides. The only way to determine whether a neces- 
sary characteristic be a property, is to ascertain whether it be 
something additional to our conception of the object. Accord- 
ingly, we say that it is the property of a circle to contain a 
greater extent of surface for the length of its boundary than 
any other plane figure, and of man to be a member of political 
society. 

While property is always attached to an essence, or species, 
this connection may immediately relate either to that generic 
part which the species has in common with other species, or 
to some peculiarity in the "difference" of that one species. 
Hence properties are of two sorts, the generic and the specific, 
or differential. Mortality is a generic property of man, as an 
animal ; the power of using language is a specific property of 
man, as the rational animal. 

6. The fifth, and last, predicable is "accident." It is that 
which pertains to an object, or entity, yet which is not neces- 
sarily connected with the nature of the object. The faculty 
of language and the power of laughter are properties of man, 
while the act of laughing and that of speaking are accidents ; 
because a man is not always laughing and speaking. 

Moreover, we must rank with accidents any ascript concern- 
ing which we cannot tell whether or not it is necessarily in- 
volved with the nature, or essence, of the subject; although 
such an ascript is not an accident in the full and proper sense 
of the term. For it resembles accident, and it is unlike prop- 
erty and attribute, in this important respect, that it cannot be 
inferred from the mere existence of the subject. But, in the 
full sense of the word, that only is an accident which is known 
to be separable from a nature, or essence. 



58 THE MODALIST. [Chap. VII. 

This separability, however, means only that an accident is 
not a necessary consequent or concomitant of the nature of 
the subject. It does not mean that every accident is insepa- 
rable from the object which may have the given nature. With 
respect to this object an accident may be either separable or 
inseparable. It was accidental to Voltaire, considered as a 
man or as a genius, to be born in France ; yet this fact was 
inseparable from the man. It was, also, an inseparable acci- 
dent of Socrates, as the father of Grecian philosophy, to be a 
statuary. So, on the supposition that there are no human 
beings except those born on this planet, it would be an insepa- 
rable accident of man to be a native of the earth ; for, so far 
as their nature is concerned, human beings might be born 
elsewhere. The inseparable ascript of a class of things, how- 
ever, is seldom conceived of as an accident. It is found to be 
connected in some way with the nature of the subject, and is 
regarded as a property. 

We must not leave this fifth predicable without noting how 
the term "accident," as here opposed to "genus," "difference," 
"species," and "property," is much more limited in applica- 
tion than when it is opposed to "substance," or "being." The 
accidents of a thing simply as an entity include everything 
whatever that can be predicated of it. The reason for this 
is, that an entity, simply as such, is not necessarily one kind 
of thing rather than another, so that every addition to our 
thought of it is, in a sense, accidental. This wide signification 
of "accident" — as equivalent to "ascript"' — is easily distin- 
guished from its ordinary logical meaning, though the two are 
by no means disconnected. 

In discussing the five predicables we have used objective 
rather than subjective language, following the ancient manner 
of speaking. We have mentioned genus, species, difference, 
property, and accident, rather than generic, specific, differen- 
tial, proprietal, and accidental, conceptions. In the primary 
and literal sense of words it is not things, but notions, as 
representative of things, that are predicable. Yet the ancient 
mode of expression serves to remind us that the logician 
always considers thought objectively, even while he may be 



Chap. VII.] PREDICATIVE NOTIONS. 59 

studying our varying conceptions of the same thing or kind of 
thing. For these vary only because we contemplate an object 
now in one aspect and in one set of connections, and now in 
another aspect and in another set of connections. 

7. The classification of predicative conceptions under the 
five predicables applies only to those cases in which the exact 
logical connection of the predicate with the nature of the 
subject is part of our thought. We can, and often do, make 
assertions without determining whether the predicate be a 
genus, or a species, or a difference, or a property, or an acci- 
dent. The doctrine of the predicables, therefore, is not so 
widely applicable as that of the categories. 

Every " predicable " presupposes one of the categories, and 
then makes an addition to it. For it presents some ascript, 
not simply, but as related in some one of five ways to the 
nature of the subject. The predicables, therefore, are of the 
same radical nature with the category of relation ; yet they 
are properly discussed by themselves on account of their func- 
tional connection with all the categories, and because of their 
logical importance. 

Evidently the end and use of these complex modes of con- 
ception is to state the manner in which any ascript is logically 
related to the nature of a subject ; for they always set forth 
something, either as the whole essence of a substantum, or as 
included in the essence, or as attached to it. The predicables 
are those forms of predicative thought which we naturally 
employ after obtaining thorough information regarding the 
logical relations of a subject ; while the categories are those 
more simple and primary forms of conception by which truth, 
whether individual or general, is set forth without reference 
to the logical connection of things. 

8. Logicians speak only of five predicables ; yet some other 
conceptions — especially "attribute" and "adjunct" — are of 
the same general character. Anything included in either genus 
or difference — that is, any part of the species, or essence — 
is, technically speaking, an attribute. Attributes, therefore, 
are either generic or differential. A nature consists of the 
sum of its attributes. Whatever is connected with a nature 



60 THE MOBALIST. [Chap. VII. 

without being a part of it, is an adjunct. Every adjunct, of 
course, is either a property or an accident. 

" Quality " is also a kind of predicable, and nearly the same 
as attribute. It is properly that mode of conception which 
sets forth " what kind of a thing " the subject may be ; that 
is, which assigns to the subject a generic (or a differential) as 
distinguished from a specific, nature. But, with a somewhat 
wider use of language, whatever does or may permanently char- 
acterize is called a quality. Hence properties sometimes receive 
this name, because by enlarging our conception they may be 
taken within the nature. When quality is used to set forth 
nature or character simply, and without reference to logical 
connections and classifications, it is a "category," not a 
" predicable." 

We have seen that, for most logical purposes, the categories 
may be reduced to two classes, — the substantal and the ascrip- 
tional, — and that these may be made to replace one another 
in assertions. In accordance with this, we now add that any 
one of the predicables may be expressed by either substance 
or ascript. We may say either, "John is a man," or "is 
human"; "is rational," or "is a rational being"; "is a biped," 
or " has two legs " ; " is a European," or " was born in Europe " ; 
" wrote that note," or " was the writer of that note," intending 
by our language to set forth either genus, difference, property, 
or accident. We more naturally express genus and species 
substantally, and the other predicables ascriptionally ; but 
either may be expressed either way. 



Chap. VIII. ] THE DEFINITION OF NOTIONS. 61 



CHAPTER VIII. 

THE DEFINITION OE NOTIONS. 

1. Clearness and distinctness radically the same. Definition and divi- 
sion defined. 2. Definitions are either essential or accidental. 3. Some, 
necessarily, are accidental, or relational. 4. Essential definitions are either 
exhaustive or selective ; 5. Scholastic or notational ; 6. Adequate or 
inadequate. 7. Nominal and real definitions. 8. The essence of a thing 
is either (a) its whole form, or constitution, (5) its form so far as conceived 
of by us, or (c) the prominent and important part of its constitution. 
9. " Substantial forms." Singular essences. 

1. Clearness and distinctness shonld not be contrasted as 
radically different. Distinctness is simply clearness consid- 
ered as enabling ns to make correct distinctions. Whenever a 
thing is clear, it is also therein distinct. Sometimes, however, 
we say that an object is apprehended clearly when its several 
parts and boundaries are perceived ; and that it is apprehended 
distinctly when these are exactly and perfectly perceived. In 
this contrast distinctness is the highest attainable degree of 
clearness. 

Definition and division are processes whose chief aim is to 
Tender our conceptions as clear, or distinct, as possible. Each 
contemplates every object as a whole ; but definition regards 
in turn the several elements of an object, as they are severally 
related, and then presents these in <a connected statement ; 
while division studies a number of objects more or less similar 
in their nature, with respect to their points of agreement and 
of difference, and then arranges them according to their agree- 
ments and differences. 

In saying that we attentively consider objects in these opera- 
tions, we mean only that we scrutinize things in idea, not that 
any entities are actually examined. If, indeed, we have no 
reliable knowledge of an existing object or set of objects, we 
should make it the subject of our enquiries and observations. 



62 THE MODALIST. [Chap. VIII. 

The science of logic directs one to such investigations, and 
gives useful directions concerning them. But the processes 
of which we now speak presuppose a certain kind or degree of 
knowledge, and merely aim to give the ideas we have so 
definite a shape, that we may both be free ourselves from con- 
fusion or unreadiness, and be able to guide others into a cor- 
rect understanding of oar conceptions. The attempt to form 
a definition or division may bring to light the inadequacy of 
our information, and so lead us to remedy that deficiency. But 
definitions and divisions of themselves pertain properly only to 
the perfecting of notions formally. Finding that one knows, or 
conceives, of an actual or possible class of things, and without 
enquiring whether the things really exist or not, definition 
gives an internal, and division an external, distinctness to our 
conceptions. 

The final result, or product, of either process takes the same 
name with the process itself, and is called a definition, or a 
division. In each case, also, it is expressed by an identifying 
statement. A definition identifies an object considered con- 
cretely, or without analysis, with itself as distinctively charac- 
terized, '/while a division identifies a generic class with the 
species contained in it. The character, however, of both pro- 
cesses is fairly stated when we say that a definition sets forth 
the nature, or essence, of a thing, while divisions set forth 
the different species of things that are of the same genus. 

2. Let us now confine our discussion to definitions, and let 
us consider four distinctions which may illustrate their nature 
and use. First, we say that definitions are either essential or 
accidental. The essential definition sets forth the nature of a 
thing directly, and is the result of an analysis. It either enu- 
merates attributes or gives genus and difference. The acciden- 
tal definition, on the other hand, sets forth the nature of a 
thing indirectly and by means of a suggestion. It makes 
use of properties or accidents. Should we say that " man is 
the rational animal," this would be an essential definition ; it 
would be an accidental definition to say that " man is the re- 
ligious," or " the political," or " the talking, animal." In min- 
eralogy the diamond would be defined by its essence as a 



Chap. VIII. ] THE DEFINITION OF NOTIONS. 63 

brilliant stone formed by the crystallization of carbon, but by 
one of its accidents, if it should be called the most precious 
of gems. 

The question whether a definition be essential or accidental 
cannot be determined simply from the definition itself, but is 
connected with the aspect under which the object may be made 
the subject of our enquiries and assertions. Ordinarily an 
essential conception embraces what appear, from the most 
general point of view, to be the permanent and distinctive 
characteristics of a thing. But sometimes our study is con- 
fined to a particular point of view, so that our discussions 
relate only to some limited aspect of the subjects considered. 
Especially a science or art may describe objects in a technical 
and peculiar way, while yet such descriptions must be accepted 
as essential definitions, so far as that branch of knowledge is 
concerned. For they set forth the natures of things according 
to that science. Linnaeus, thinking of man only as an animal, 
defined him as "the two-handed mammal." In chemistry 
laudanum is a vegetable extract of a given molecular consti- 
tution ; in Materia Medica it is a poison operating in a specific 
way. Each science may determine its own distinctive con- 
ception of an object ; and then the essence is that in the 
object which corresponds to this conception. 

The term "accidental," as applied to definitions, is used in 
a wide sense which relates to all adjuncts, whether properties 
or accidents. For properties, even more than accidents, are 
used in accidental definitions. Indeed, these might be advan- 
tageously styled relational, or afunctional, definitions, as they 
use what is related, or joined, to the essence. 

3. Some logicians, with some reason, say that the accidental 
definition does not define, but only determines, a conception. 
The question is one of terms. Ordinarily and pre-eminently, 
a definition is an analytical statement ; yet, if every proposi- 
tion which fixes the meaning of a word by giving, directly or 
indirectly, the essence of a thing, may be called a definition, 
then we must admit accidental definitions. These are espe- 
cially necessary in discussions concerning things simple and 
incapable of analysis. For in no case can the duty of giving 



64 THE MODALIST. [Chap. VIII. 

a clear conception be avoided by saying that the thing is simple 
and ultimate, and does not admit of definition. Every con- 
ceivable entity can be determined by means of its adjuncts or 
relations ; and, if it be simple, it ought to be defined in this 
way. Hence it is proper to say, " Space is that abiding kind 
of entity in which all other things exist, and in which motion 
takes place"; "Time is that fleeting kind of entity during 
which events transpire, and by reason of which they are related 
as past, present, and future " ; " Belief is an intellectual 
state differing from conception, specially conditioned on the 
thoughts of existence and non-existence, and expressed by the 
assertive proposition " ; " Sensation is a psychical experience 
caused by the action of certain nerves, and is the condition of 
our perception of material things and qualities." 

Accidental definitions are also useful when the object, though 
complex, is not easily described, or when there is no need for 
specific description. One might say that the guillotine is the 
instrument by which capital punishment is inflicted in France. 
But since this statement would not give the " essence " to one' 
unacquainted with the construction of the guillotine, it does 
not deserve the name definition as well as those statements by 
which simple natures are indicated relationally. 

4. The next distinction pertains to essential definitions only, 
and, in the remainder of this discussion, these will chiefly 
occupy our attention. 

The essential definition is either exhaustive or selective. In 
the former case it sets forth all the attributes belonging to a 
subject as having a specific nature; in the latter, only the 
more distinctive and important characteristics. It would be 
an exhaustive definition of a circle to say that it is a plane 
figure bounded by a curved line which returns into itself, and 
which is everywhere equally distant from a point within. 
Promptitude might be exhaustively defined as the habitual 
disposition which leads one to decide and act at once when the 
proper occasion has come. But it is a selective definition to 
say that man is the " rational animal," for we always think of 
man as having a certain bodily shape and size, and as having 
a practical and affectional, as well as a rational, nature. De~ 



Chap. VIII.] THE DEFINITION OF NOTIONS. 65 

fining coal as "a black combustible mineral widely used as 
fuel," this would sufficiently express our ordinary conception 
of that substance. The same would be true if we should say 
that coal is " a geological vegetable deposit largely composed 
of carbon." 

In one sense substances, especially material substances, 
admit only of the selective definition, for we always regard 
them as possibly having other attributes than those which we 
know them to have. Iron has chemical, medicinal, and mag- 
netic powers of which the ancients knew nothing, and prob- 
ably has other qualities not yet discovered. Yet all these 
qualities are allowed for in our conception of the permanent 
nature of this metal. Our notions of substances, therefore, 
though they may be accurate and reliable, are never analyti- 
cally complete. But our definitions of powers, spaces, times, 
figures, relations, and other non-substantial entities may be 
exhaustive ; that is, they may give every part of the constitu- 
tion of the object as conceived of by us. 

5. In the next place the essential definition may be either 
scholastic or notational. The scholastic definition, which is that 
commonly discussed in logic, is effected by giving the genus 
and difference of a thing. In other words, it uses two com- 
prehensive conceptions, one of which presents the essential 
attributes of a genus, and the other the distinguishing attri- 
butes of a species. This mode of definition is naturally fol- 
lowed when the generic characteristics of a new kind of thing 
are easily known, while some care is necessary io determine 
its difference from other species of the same class. We per- 
ceive at once that an oak or a beech, a pine or a cedar, is a 
tree ; then we proceed to say how it is distinguishable from 
other trees. We at once recognize oxygen or hydrogen as a 
gas ; then we enquire what are its differential peculiarities. 
Moreover, in lectures and discussions, definition by genus and 
difference is a clear and compact mode of statement. 

At the same time this is not the only proper mode of defini- 
tion. The notational method, which simply enumerates attri- 
butes (or essential marks) without any reference to genus 
and difference, is equally correct with the scholastic, and is 



66 THE MODALIST. [Chap. VIII. 

often employed to advantage. It is less artificial than the 
scholastic. 

6. Another distinction discriminates between adequate and 
inadequate definitions. A definition is adequate when it imparts 
a distinct understanding of the nature to be defined. Exhaus- 
tive definitions are adequate when they are expressed simply 
and without superfluous additions. Selective definitions suffice 
when they present the most important and distinctive attri- 
butes. Hence the scholastic definition gives both genus and 
difference ; for neither of these by itself would distinguish, and 
each is supposed to contain some fundamental marks. The 
two together present the whole nature ; though they may not 
give it exhaustively, but representatively. Hence, too, insignifi- 
cant marks cannot be the basis of definition ; for they are not 
"essential" in the sense of being important. "Man is the 
two-handed mammal," is an inadequate definition of human 
beings, unless we limit our thought to the sphere of natural 
history. The question of the adequacy of a definition depends 
on the question whether it clearly sets forth that conception 
of a thing which we wish to use. 

7. Finally, definitions are either nominal or real. Logicians 
differ in their explanations of this distinction. Some say that 
the nominal definition sets forth the meaning of words, and 
the real, the nature of things. But every definition, though 
pertaining immediately to -notions, necessarily explains also 
terms and natures. Others teach that the real definition sets 
forth more of the nature of the thing than is implied in the 
name, while the nominal deals with a less comprehensive con- 
ception. The difficulty with this explanation is that the sig- 
nification of a term expands when our conception of a thing 
expands ; so that there is no good ground to distinguish our 
more contracted conceptions as nominal. 

The true difference between nominal and real definitions 
seems to be that the former simply explicate notions, without 
teaching that objects really exist of the nature described, while the 
real definition implies that there are objects corresponding to it. 
Should we describe a dragon as a winged serpent breathing 
flame, or a mermaid as an inhabitant of the sea, half woman 



Chap. VIII. ] THE DEFINITION OF NOTIONS. 67 

and half fish, these definitions would be merely nominal. 
Indeed, every definition must be treated as nominal until we 
know that it sets forth a real nature. Thus some political law 
or institution, being merely supposed to exist, might be denned 
in order that its probable operation might be accurately dis- 
cussed. 

Most definitions, however, and especially those used in 
science, are real, because they are intended to be applicable to 
actually existing objects. Therefore, also, they are more than 
mere definitions ; they are assertive, as well as explicative, 
propositions ; and on this account may be made the grounds 
of actualistic inference. Having learned that saltpetre is 
nitrate of potash, we can say that any piece of saltpetre has 
this composition and all the properties flowing from it. At 
the commencement of discussions respecting matters of fact 
one should see to it that the definitions laid down are not 
merely clear explanations of conceptions, but also truthful 
representations of things. 

8. This discussion concerning the definition may be con- 
cluded by an enquiry which may render more exact our under- 
standing of the objective significance of this form of thought. 
Let us consider what is meant by " the essence " of a thing. For 
any statement which distinctly gives the essence, either 
directly or indirectly, is therein a definition. 

The word " essence " is a Latin term, said to have been in- 
vented by Cicero in translation of oWa. It is more restricted 
and definite in its use than the Greek word ; yet it admits 
several varieties of meaning. The doctrine of the essence may 
be presented in explaining these varieties. First of all, we 
might say that the essence of a thing is its entire being, or -V 
entity, considered analytically, or as constituted of related 
parts, or elements. This would follow from the common 
statement that " the essence is that which makes a thins: to be 
what it is," provided we take these words in their full force. 
For no entity would be what it is if any of its elements were 
wanting. In this sense the essence of a thing is identical with 
its entire form, or constitution. For any entity can be viewed 
either indeterminately, that is, simply as a thing, and ivithovt 



68 THE MODALIST. [Chap. VIIL 

distinction of parts or elements; or its parts may be individu- 
ally and definitely conceived of. Entity as viewable in the one 
way has been called " matter" and as viewable in the other way 
has been called "form" ; while, as conceivable in both ways 
at once, it is both matter and form. Essence, therefore, may 
sometimes signify the entire form, or constitution, of a thing. 
This, however, is an extreme use of the term. 

Commonly by " essence " we do not mean the whole consti- 
tution, or. make-up, of a thing, but only that constitution so far 
as it is actually conceived of by us. For, ordinarily, our thought 
of an object is not exhaustive of everything contained in the 
object, but takes in only such characteristics as have engaged 
our attention. Hence only so much of the constitution, or 
constituents, of an entity, as we conceive of determinately is 
called the essence ; while the rest is treated as so much mat- 
ter, or indeterminate entity. For example, all the particulars 
included in our conception of water would be, for us, the full 
essence of water ; though we may allow that other attributes 
may belong to the nature, or form, of water, in its absolute 
totality. 

Finally, essence may mean something less even than the 
nature of a thing so far as conceived of. For often a few of 
the prominent and controlling elements of that nature are 
taken as the representatives of all, inasmuch as the rest may 
be inferred or supposed where these are found ; in short, we 
limit our thought to what might be called the representative, 
or symbolic, essence. Hence man is denned as the "rational 
animal." 

The first of the three significations now given may be 
rejected as improper ; it is better expressed by speaking of the 
entire nature, or form, of a thing. The other two significa- 
tions are often employed. Using them only we distinguish 
the complete and the representative essence ; the former being 
set forth by the exhaustive, and the latter by the selective, 
definition. For an exhaustive definition gives every part of a 
thing as conceived of by us, though not necessarily every part 
of a thing. 

According to the foregoing the idea of essence is properly 



Chap. VIII.] THE DEFINITION OF NOTIONS. 69* 

of more restricted application than that of form, or nature, or 
constitution. But, of course, when we speak or think of an 
essential form, or nature, we mean simply an essence. 

9. Ancient logicians used to mention the " substantial 
form," and they distinguished this from the substance (or 
substantum) on the one hand, and, on the other, from the 
essence, and even from the entire form. So far as the phrase 
embodies truth a substantial form is a substantum considered 
as having a given essence or form, that is, as more or less ana- 
lytically, or determinately, conceived of. But substance, as 
contrasted with substantial form, was entity viewed independ- 
ently, yet not determinately, but only as ready for determina- 
tions — that is, entity viewed merely as entity, merely as a 
"thing." This distinction has been found needless in modern 
philosophy. By substance, or substantum, we now mean any- 
thing whatever considered independently and as fitted to be 
the subject of predication, whether it be already characterized 
— that is, conceived of definitely — or not. 

Some have taught that the essence of a singular thing does 
not include any of its singular characteristics, but only such 
as may belong to it as the member of a species ; and that, 
therefore, the species of an individual thing and its essence 
are always identical. It is true that, in our discussions, things 
are commonly conceived of as having specific natures, and are 
defined only in that light, and as having a specific essence. 
We might say, for example, of some assertion that it is, essen- 
tially, a lie. Yet — so far as we can see — any statement in 
which the leading features of a singular conception are set 
forth may be said to give the essence of the singular object, 
and may be called the definition of that object. Thus it would 
define Bucephalus to say that he was "the spirited horse 
which Alexander the Great tamed and rode." 

Here, too, a false distinction concerning essences may be 
briefly mentioned. It pertains only to material or spiritual 
essences, and not to those of substanta, or logical substances, 
in general. Locke, in particular, teaches that every substance w 
has two essences, the " nominal" which is perceivable by us 
and is set forth in names and definitions, and the " real" which 



TO THE MODALIST. [Chap. VIII. 

is the underlying but incognizable basis of the knowable 
essence. This doctrine is connected with the mistaken view 
that substance is the incognizable substratum in which active 
and passive qualities inhere. Both theories must be rejected 
as philosophical fictions. Every substance may have qualities 
as yet unknown to us, but we have no reason to say that these 
qualities are unknowable, or that they are the origin of those 
known. The truth seems to be that Ave may understand the 
real and ultimate nature of any kind of substance, though, it 
may be, not exhaustively. There may be a difference, of course, 
between the constitution of a substance so far as known and 
that total constitution which is only knowable. But this does 
not justify the theory of a knowable and an unknowable 
essence. 



Chap. IX.] LOGICAL DIVISION. 71 



CHAPTER IX. 

LOGICAL DIVISION. 

1. Aims to render conceptions distinct and definite. A succession of 
synthetic acts. 2. To be distinguished from didactive and from rhetorical 
division. 3. Indispensable that the dividing members exclude one another. 
4. Division should relate to one "principle." 5. Specially useful if the 
principle be an " added mark." G. Certain exceptions to this rule. 7. The 
dividing members should be co-ordinate ; but this is not an absolute law. 
8. The division in certain cases should be exhaustive. 9. Dichotomy, or 
'•inhnitation," a comparatively profitless division. 

1. The second logical process by which our conceptions are 
rendered distinct is called " the division of notions." This 
process takes any collection of conceptions which have a com- 
mon generic part and co-ordinates them — or rather the con- 
cepta corresponding to them — into subordinate genera and 
species, according to their agreements and differences. After 
" paper " has been defined as a " fibrous material manufactured 
into sheets from the pulp of rags, straw, or wood, by a process 
of spreading, pressing, and drying," one's conception, either of 
paper in general or of any kind of paper, becomes more dis- 
tinct, if we enumerate the various kinds, and compare them 
with one another. Eefiection on the peculiarities of writing- 
paper, wrapping-paper, wall-paper, building-paper, hard-pressed 
paper, drawing-paper, and tissue-paper, as well as on the char- 
acter common to all these varieties, frees one's ideas both of 
paper and of kinds of paper from an indefiniteness which often 
beclouds unelaborated thought. 

The name "logical division " literally indicates the mental 
separation of a generic class into its component species, but it 
is metonymically used to indicate the formation of specific 
conceptions from a generic conception by the successive addi- 
tion of differences. For we speak of the division of a generic 
notion. This process, however, though involved in the divis- 



72 THE MODALIST. [Chap. IX. 

ion of a class, is not really divisive, or separative ; it is addi- 
tive, or synthetic. 

2. Logical division is not to be confounded with that 
didactive division by which the heads of a treatise are dis- 
tinguished and arranged. These processes are of a kindred 
nature, but they aim at different results. Logical division sets 
forth methodically the principal agreements and differences 
which exist within some generic class. With this end in view, 
we may regard that class in various lights, and divide it in 
different ways. A people may be classified according to their 
diversities in political opinion, in religious belief, in business 
occupation, in sex, or in age, or in color, or in any other respect ; 
and, in order to a thorough knowledge of that people, they 
should be considered in all these respects. But in planning an 
account of them one need not follow any one of these divis- 
ions, but should simply arrange his thoughts in the order best 
suited for the conveyance of his information. 

At the same time it is to be borne in mind that a scientific 
treatise gains in lucidity if its more fundamental distinctions 
be expressed by logical divisions ; and commonly the order of 
its discussions wisely refers to one or more of these divisions. 
For instance, President Woolsey, in one of the opening chap- 
ters of an excellent treatise, divides International Law first 
into Public and Private ; then again, into the Law of Eights 
and Obligations and the Law of Claims and Duties ; and then, 
finally, into the Law in Time of Peace and the Law in Time of 
War ; after which he adopts an order of discussion based on 
this last division. But he might have chosen some other order 
had he seen fit. 

The oratorical arrangement of thought, which aims at con- 
viction and persuasion rather than instruction, is yet more 
separated from logical division than any arrangement which is 
merely didactive. 

3. In order that logical division may fully effect its purpose, 
several rules are given, of which, however, one — and only one 
— is so fundamental as to admit of no exception. This is, 
that the dividing members of the genus must be exclusive of one 
another. In other words, the specific natures in any logical 



Chap. IX.] LOGICAL DIVISION. 73 

division must be such, that no two of them can belong to the 
same individual subject. To divide the genus "book" into 
the " folio," the " quarto," the " French book," the " German 
book," the " reader," the " dictionary," and so forth, would 
violate this rule ; because the same book might have two or 
more of these natures. Again, to divide " moral actions " 
into "right" and "'wrong," or into "public" and "private," 
would be a good division. In either case conflictive natures 
would be presented. But it would not be a division to say 
that " moral actions are either right or wrong or public or pri- 
vate " ; for these four species of moral actions, though dis- 
tinct, are not separate. 

It is useful to compare individuals of different species to- 
gether when the species are not conflictive ; or to compare the 
same individual as being of one species with itself as being of 
another species also. A quarto and a dictionary might be 
compared in a way to bring into prominence their common 
part and their peculiarities. But this is a more analytical and 
delicate operation than the one under consideration. Logical 
division recognizes that natural separation of classes which 
results from the fact that mutually repugnant natures may be 
successively united to a generic nature ; and which, therefore, 
immediately shows, with respect to the members of each spe- 
cies, both what a thing is and what it is not. This process, 
which at once characterizes and distinguishes things, is easily 
apprehended ; and is of great service especially at the begin- 
ning of a discussion. 

4. A second rule, nearly equal in importance to the first, is 
that the division should refer to one principle, or fundamentum. 

The word " principle," here, is used in a special sense. Often 
it signifies a general truth used as a premise in argument, or 
reasoning ; here it designates a generic characteristic to which 
a specific difference may be immediately attached. The com- 
mon character " sex " belongs to all quadrupeds ; and, with 
respect to sex, they may be divided into male and female. 
Mankind, with reference to that capability of culture which 
distinguishes them all from brutes, are divided into the enlight- 
ened, the civilized, the semi-civilized, the barbarous, and the 



74 THE MODALIST. [Chap. IX. 

savage. In saying that a division should rest on one principle, 
or basis, we mean that the same characteristic should be used 
successively with the several differences, so as to form the 
several species. The same thing is meant when we say that 
division should rest on one fundamentum. But this application 
of the word " fundamentum " must be distinguished from its 
use in connection with comparison, and with the perception of 
relations generally. In the latter case a fundamentum is one 
of the things related, considered as the foundation of the rela- 
tion ; so that comparison calls for two fundamenta at least ; 
logical division requires but one. 

The rule that only one principle of division should be used 
is somewhat auxiliary to the rule that the species should be 
mutually exclusive. For example, if we take only one funda- 
mentum for the division of the human family, — say race, or 
country, or language, or religion, or sex, or age, or condition in 
life, — it is easy to form a classification in which the members 
will be exclusive of one another. But if a division uses first one 
and then another principle, the species. will be likely to overlap. 
To divide the people of the British Isles into English, Scotch, 
Welsh, Irish, Protestants, and Boman Catholics would be a 
violation of the first rule resulting from a neglect of the second. 

The principal advantage, however, of adhering to one funda- 
mentum is not the aid which this rule gives to others, but its 
direct effect in adding to the clearness of our conceptions. 
This result takes place in a twofold way. First, the consider- 
ation and comparison of the different species brings the prin^ 
ciple of division into distinct vietv. Dividing men into Jews, 
Mohammedans, Christians, and Pagans, we see that man in 
general is a religious animal, and that this religiousness is 
something different from any particular form of faith. Then, 
secondly, through comparison of the difference which belongs 
to each specific religion with the peculiarities of the other 
forms, we are led to perceive exactly the character of each. 
Divisions thus made often have the effect of definitions, and 
may even be considered a kind of " accidental " definition. For 
they present both the principle of the division and the con- 
stituent species in determinative relations to one another. 



Cii-vr. IX.] LOGICAL DIVISION. 75 

5. Some say that the " fundamentum divisionis " should 
always be an essential mark — an attribute — of the genus to 
be divided ; others say that it should be an " added " mark, that 
is, some adjunct of the genus. The truth is that it may be 
either ; though more frequently it is an added mark. In the 
above illustration the religiousness of man is a property, not 
an attribute. Classifications based on an added mark are 
especially helpful when we would study some general nature 
in an enlarged aspect which includes more than its essence, 
or ordinary definition; as, for instance, when we consider 
human beings as religious ; for in this we have added some- 
thing to their essence. 

But that an attribute as well as an " added mark " may be 
the fundamentum of a division may be easily shown. When 
" rectilineal figures " are divided into " three-sided," " four- 
sided," " five-sided," and so on, the differences are successively 
attached to the attribute of having straight sides. After the 
same manner we divide color into white, black, red, blue, yel- 
low, and so forth. In this latter case, since the nature of the 
genus may be regarded as simple and as containing only one 
attribute, it is all used as a " fundamentum divisionis." 

6. We must add, however, that certain classifications of 
natural objects seem to attach their differences to a variety 
of fundamenta. These are cases in which Nature herself in 
diverse ways has made additions to a complex of attributes. 
We divide the genus " gas " into oxygen, the life-supporting 
gas ; hydrogen, the lightest of gases ; nitrogen, the most inert 
gas ; and chlorine, the colored gas. Vertebrate animals are di- 
vided into mammals, birds, fishes, and reptiles. Quadrupeds — 
though they may be divided according to one principle, as, for 
example, into graminivorous, carnivorous, omnivorous, and so 
forth — are ordinarily classified as the elephant, the rhinoceros, 
the hippopotamus, the horse, the cow, the dog, the cat, and so 
on. In such divisions the leading peculiarities of each species 
are attached to the genus not immediately, but through a fun- 
damentum used only, or chiefly, for that species. For instance, 
all vertebrate animals bring forth young; mammals bring 
forth their young alive : all have some natural covering and 



76 THE MODALIST. [Chap. IX. 

style of locomotion ; birds are covered with feathers and fly in 
the air : all have a proper habitat where they live and breathe ; 
fishes live and breathe in the water : all have a bodily structure 
which determines their modes of activity ; reptiles are so made 
that they crawl upon the belly. A division, therefore, which 
uses different fundamenta in the formation of its species cannot 
be rejected as incorrect, provided only its members exclude one 
another ; as they do in the above classification of animals. 

7. A third rule of logical division is that the dividing mem- 
bers should be co-ordinate ivith one another ; in other words, the 
several species into which any genus is immediately separated, 
should show the same amount of difference added to the common 
character. This direction is especially to be observed in natu- 
ral history and in all -classifications which are designed to set 
forth the nature of things as exactly as possible. It may, 
however, be often dispensed with in divisions which aim only 
at clearness of statement. It would be a violation of this rule 
if animals were divided into invertebrates, reptiles, fishes, 
birds, quadrupeds, quadrumanes, and the biped, man. The 
first of these species would not have enough added difference, 
and the last three would have too much, to make them co- 
ordinate with the other classes mentioned, and with each 
other. Correct division first distinguishes animals into the 
vertebrate and the invertebrate ; then vertebrate animals into 
reptiles, fishes, birds, and mammals ; and then mammals into 
quadrupeds, quadrumanes, and bipeds. 

But frequently distinctness of statement does not require 
that the component kinds should be co-ordinate ; the attempt 
to make them so may even savor of undue refinement. Plane 
triangles are rightly divided into the equilateral, the isosceles, 
and the scalene, though, according to the rule, we should first 
distinguish triangles which have some sides equal from those 
which have no sides equal, and then subdivide the first class 
into the isosceles and the equilateral. In like manner, gram- 
marians properly classify words as monosyllables, dissyllables, 
trisyllables, and polysyllables. Nothing would be gained by 
dividing them, first into those of one syllable and those of 
more than one, and then subdividing this latter class. 



Chap. IX.] LOGICAL DIVISION. 77 

8. One other rule remains: the division should be exhaustive; 
in other words, the dividing species, taken together, should 
equal the whole genus divided. But this completeness of 
classification, though an excellence to be desired, is indispen- 
sable only in certain cases. 

Sometimes an exhaustive enumeration is needed for practical 
purposes. A treatise on mortgage investments should indicate 
all the various ways in which a loan might prove unsatisfac- 
tory. The money might be lent on security of insufficient 
value ; or on land with a bad or doubtful title ; or on property 
burdened with previous mortgages ; or where taxes, court- 
judgments, or mechanics' liens detract from the security. The 
papers might not describe the property adequately; or they 
might not be legally drawn-up and executed ; or they might 
not have been recorded duly and in proper time. Then, also, 
faithless or incapable agents, tricky or shiftless borrowers, 
unwise local laws, or inefficient tribunals, may render it unde- 
sirable to make a loan. A person with money to lend should 
think of all these things, and so avoid, as far as may be, every 
cause of loss or annoyance. 

Complete enumeration is also necessary ivhen ive icoidd rea- 
son disjunctively to a definite conclusion. In a trial for murder 
the prosecutor might say that one man may kill another either 
accidentally, or in self-defence, or through passion, or through 
deliberate malice, and then argue that it could not be in either 
of the first three ways, and therefore must be deliberate mur- 
der. This reasoning would be defective because of incomplete 
enumeration. The killing might have resulted from insanity, 
or from some hallucination. 

In science exhaustive classifications give satisfaction because 
of the completeness of view and treatment for which they pre- 
pare. Yet such classifications can be hoped for only in those 
departments of knowledge whose boundaries and provinces have 
been accurately ascertained. Many fields of investigation — 
such as botany, mineralogy, natural history, and others, — do 
not admit of it. In these sciences we classify all we know, 
but expect to find species as yet unknown. 

9. A truly exhaustive division is based on a pervading and 



78 THE MODALIST. [Chap. IX. 

comprehensive intelligence, every species in a genus being 
distinctively conceived of. We do not, therefore, give this 
character to a process sometimes called " dichotomy " ; because 
it divides either all things in general, or all the individuals of 
a genus, into two classes : it is sometimes also called " infini- 
tation " ; because it conceives of one of the classes as "infinite," 
or rather as " indefinite," in extent and character. Evidently 
all things whatever are either of some given kind or things 
not of that kind ; and any genus consists of the individuals 
of some one species and others not of that species. Man and 
not-man may be said to make up the universe, and animals are 
either quadrupeds or not-quadrupeds. This dichotomy is 
often useful in argumentative statements, but it throws little 
light on the nature of things, and is of small value as a logical 
division. It may also be used as a test when the question 
arises whether each member of a division excludes all the rest. 



Chap. X.] PROPOSITIONS AND PREDICATIONS. 79 



CHAPTER X. 

PKOPOSITIONS AND PREDICATIONS. 

1. Judgment involves both conception and conviction. The proposition 
defined. 2. A proposition is not always an assertion. Predication defined. 
3. Propositions are either enunciative or assertive ; 4. Affirmative or nega- 
tive ; 5. Presentential or inherential (the predication proper) ; 6. Verbal 
or mental; 7. "Categorical" or "conditional" ; 8. Actualistic or hypo- 
thetical. 

1. Having discussed the notion, or conception, we pass to 
the judgment, or assertion. This is the second general mode 
of rational mental action. Ordinarily judgment signifies the 
formation of a probable belief : in logic it is the act of forming 
any conviction whatever. The most absolute demonstrative 
conclusion, and even the immediate perception- of fact, are in- 
cluded under this term. Should one look upon a rose and say, 
" The rose is red/' this would be a judgment. 

Both the primary powers of the mind, thought and belief, 
are exercised in judging. We first conceive of a thing existen- 
tially, — that is, think of it as existing or as non-existent, — and 
then, exercising conviction along with this conception, we 
assert that the thing is, or that it is not. 

That form of words in which a judgment is fully expressed 
is called a proposition ; and this name is also given to that 
construction of thought in which a judgment is embodied. 
Propositions in words, however, are important only as they 
are related to propositions within the mind. 

A mental proposition is essentially of the same nature with 
an existential conception, but it is more analytical and brings 
the idea of existence, or of non-existence, into prominence. 
To believe in " God " is the same as to believe in " God as 
existing"; and this belief is fully expressed by the proposi- 
tion, " there is a God," or " a God exists." 

2. Propositions are not always assertions. In themselves 



80 THE MODALIST. [Chap. X. 

they are only the forms of thought which judgments employ. 
At the beginning of every criminal trial two propositions are 
presented to the jury, "the man is guilty" and "the man is 
not guilty." Neither of these embodies a judgment at first, 
but one or the other does so when, after the hearing of evi- 
dence, it becomes the verdict of the jury. 

While the term " predication " also designates the form of 
thought employed in judgments, it implies further that the 
existential conception, or proposition, is not only entertained, 
but believed in, or asserted. The difference between "predi- 
cation " and " proposition " may be traced to the primary sig- 
nification of these terms. Originally a proposition signified 
a statement placed before one for his acceptance or considera- 
tion, while a predication meant a statement in which some fact 
was made known or published. Hence "proposition" came 
to refer specially to the thinking person, and "predication" to 
the objects thought of. But as a statement about things is 
more closely allied to the exercise of conviction than a state- 
ment of one's ideas, the notion of assertion was always re- 
tained in connection with the thought of predication, while it 
was often disconnected from the thought of a proposition. 

3. We are now prepared for certain distinctions by which 
propositions are logically divided, and which illustrate both 
the radical nature of judgment and the various modes in 
which judgment takes place. 

The first of these, emphasizing the truth that even existen- 
tial thought may be unattended by conviction, divides proposi- 
tions into the enunciative and the assertive. At the opening of 
every debate it is proper to state the " question." Then two 
contradictory propositions are before the " house " ; for exam- 
ple, that " a protective tariff should be maintained," and that 
"it should not be maintained." Up to this point the propo- 
sitions are mere enunciations ; either of them becomes asser- 
tive when it is upheld by its advocates as true, or is accepted 
as true by those who have weighed the arguments. 

The assertive proposition does not always set forth a thing 
as fact, or even as indisputably true, but it always expresses 
belief of some kind or degree. It is never the mere statement 



Chap. X.] PROPOSITIONS AND PREDICATIONS. 81 

of a thought, or of a question. Should one venture the opin- 
ion that "$100,000 would be a comfortable fortune/' this would 
be an assertive proposition, though it would not set forth fact, 
but merely what would be fact if one had that amount of 
money. 

The science of logic deals mainly with assertions. The 
enunciative proposition is studied exclusively for the light 
which it throws upon the assertive. 

4. A second division of propositions relates primarily to 
their assertive use, but is also applicable to them when merely 
preparations for assertion. It separates them into the affirma- 
tive and the negative, the former setting forth the existence, 
and the latter the non-existence, of things. Every predication 
is either affirmative or negative. That such is the case is 
evident ; when we are in doubt concerning a thing we cannot 
make any assertion about it ; but so soon as doubt is displaced 
by any conviction at all, we must think and believe either that 
the thing is so, or that it is not so. 

Because assertion is the most important function of proposi- 
tions, their fitness for assertion has been technically named 
their " quality " ; and so it is taught that, in quality, every 
proposition is either affirmative or negative. We should note 
that this distinction applies to those propositions called " con- 
ditional," as well as to those ordinary propositions which 
make assertions in a direct way, and which are called " cate- 
gorical." " If Gabriel be a man, he is mortal " is an affirma- 
tive, " If he be an angel, he is not mortal " is a negative, 
conditional proposition. The " quality " of such a statement 
appears, not in its antecedent, but in its consequent ; for this 
is the assertive and essential part of it. But that remarkable 
form of the conditional proposition which is styled the " dis- 
junctive," has the peculiarity of not being limited to one kind 
of " quality " ; it has both kinds, though only because it is 
itself a complex of simple conditionals. "The number is 
either odd or even," means, " If the number be odd, it is not 
even ; and if it be even, it is not odd ; but if it be not odd, it 
is even ; and if it be not even, it is odd." Two of these prop- 
ositions are negative, and two are affirmative. 



82 THE MODALIST. [Chap. X. 

5. A third distinction between propositions, though easy to 
make, is not easily expressed in any terms yet employed by 
philosophers. This must excuse our use of barbarous language 
when we distinguish the presentential from the inherential 
proposition. The presentential proposition may be defined as 
a simple existential statement ; it says simply that a thing 
exists or that it does not exist. Thus we may assert that space 
exists, or time, or that there is money or virtue ; or the oppo- 
site of these things. But the inlierential proposition sets forth 
a thing as existing in some relation; or as non-existent in that 
relation. When we say, "Virtue - is praiseworthy; money is 
useful," we assert, not the existence of virtue or of money 
(that is assumed), but the existence of the qualities of praise- 
worthiness and usefulness as belonging to virtue and money. 
In like manner, to say, " The tree grows ; the man thinks " 
sets forth the present existence of certain actions on the part 
of the man and of the tree ; while, " The tree does not grow ; 
the man does not think " sets forth the non-existence of those 
actions. To say, that " diamonds are stones " assumes the ex- 
istence of both diamonds and stones, and then asserts that 
identity exists between these two classes of things to such 
an extent that every diamond is a stone ; while to say, " Coal 
is not stone " denies — that is, asserts the non-existence of — 
identity. 

By far the greater number of statements are inherential. 
These, too, are more important, logically, than the presenten- 
tial ; for all inference and reasoning arise from the perception 
of things as existing in connective relations ; not from a 
knowledge of their mere existence. On this account, and be- 
cause the forms of language make little or no distinction 
between the two kinds of statements, only inherential propo- 
sitions have hitherto been recognized by logicians. Aristotle 
teaches that " a proposition is a sentence in which one thing is 
affirmed or denied of another." This definition does not apply 
to the presentential proposition; because a sentence which 
simply asserts the existence or the non-existence of a thing, 
cannot be said to assert one thing of another. Most writers 
since Aristotle, merely adopting his words, say, " Judgment is 



Chap. X.] PROPOSITIONS AND PREDICATIONS. 83 

that act of the mind whereby we affirm or deny one thing of 
another." Even those who have differed from him have failed 
to perceive the distinction between presentential and inheren- 
tial statements. Locke tanght — and very many have followed 
him — that judgment is the perception of agreement and disa- 
greement (or of congruence and conflict) betiveen two ideas; and 
others, in onr own day, define judgment as u the perception of 
relations." 

We prefer the ancient doctrine to either of these. Aristotle 
is right in saying that we judge respecting things, " affirming 
or denying one thing of another." Even when we judge about 
objects that are absent, or that are merely supposed, it ex- 
presses the truth better to say that we are judging about 
things than to say that we are comparing ideas : and, while 
every inherential proposition does set forth something as in 
relation to a subject, the point asserted in the great majority 
of such statements is, not that the relation exists, but that the 
predicate-object exists as related. When we say, " The man is 
wise; the man speaks," the points of assertion are, not the 
relations of the wisdom and of the speaking to the man, but 
the wisdom and the speaking themselves. Aristotle's teaching 
would have been satisfactory if he had explained that the 
affirming and the denying one thing of another are simply 
the assertion of the existence, and the assertion of the non- 
existence, of the predicate-object in its relation to the sub- 
ject-object. Yet, even with this explanatory addition, his 
doctrine takes no note of presentential assertions. 

Although the word " predication " may originally have des- 
ignated both presentential and inherential statements, usage 
and the objective reference of this word have rather confined 
its application to the inherential proposition. This is espec- 
ially indicated by our use of the term "predicate"; which is 
the name we give things as logically " inherent." The term 
"predication," therefore, might be used exclusively for inhe- 
rential assertions ; or at least, we might say that these are 
predications-proper, and then style presentential statements 
improper predications. 

6. A fourth distinction is valuable chiefly for the light 



84 THE MODALIST. [Chap. X. 

which it will throw on other distinctions yet to be considered; 
it discriminates between verbal and mental propositions. Aris- 
totle, speaking of the theory of demonstration, says that this 
theory pertains not to the external word, bnt to the word 
within the spirit — ov 7rpos tov 2£<o Aoyov, aAAa 7rp6<s tov iv rfj 
\f/vxij \6yov. He also entitles his treatise concerning proposi- 
tions Tre/ot kpfi-qviias, or De Interpretatione, showing that, in 
his view, every proposition must be scrutinized, if we would 
obtain its true meaning. 

It is, however, to be remarked that the " external word," of 
which Aristotle speaks, is something deeper and more internal 
than mere language. It is rather that thought which language 
immediately and naturally expresses, and which, therefore, 
may be called " verbal," in the absence of any better name. 
Frequently this thought is not the thought really intended to 
be conveyed, but is only indicative or suggestive of it ; and 
nothing is of more importance than to distinguish between 
that form which thought may take immediately before it is 
expressed in language, and the very essence and intent of the 
thought itself. For no mistake could be greater than to sup- 
pose that a form of statement which originally and properly 
expresses one mode of assertion may not be used with another 
logical signification. 

This may be illustrated from the fact that the grammatical 
subject and predicate of a sentence are often different from 
the true logical subject and predicate. In the sentence, 
" Caesar conquered the Gauls," the grammatical subject is 
"Caesar," and the grammatical predicate, "conquered the 
Gauls"; these would be the logical subject and predicate if 
the object of the speaker were to inform one who already knew 
of Caesar, of Caesar's conquest of the Gauls. But if it were 
only known that the Gauls had been conquered, and the ques- 
tion was, " Who conquered them ? " then " Caesar " would be 
the logical predicate, and the logical subject would be given 
in the grammatical predicate. In this case, if grammatical 
expression were conformed to logical meaning, we would say, 
"He who conquered the Gauls was Caesar." If, again, the 
hearer knew of both Caesar and the Gauls, but was ignorant of 



Chap. X.] PROPOSITIONS AND PREDICATIONS. 85 

what the one did to the other, the logical form of the sentence 
would be, "What Caesar did to the Gauls (subject), was to 
conquer them (predicate).'' The logical subject is that which 
is conceived of as already known ; the predicate is that which 
is asserted of the subject. 

For further illustration let us take the proposition, "All 
men are mortal." Grammatically and verbally, this simply 
sets forth a fact respecting all existing men; just as if one 
should say, " All the men in that village are industrious " : 
mentally and logically, it sets forth the law, " Omnibus est 
moriendum," that " man, ivhenever and wherever he may exist, 
must die." 

This use of verbal propositions to express the true and inner 
thought of the mind arises, partly from the imperfection of 
language and partly from the disposition and ability of men 
to make the same linguistic form serve several purposes. The 
circumstances of a statement generally suggest the right inter- 
pretation of it. 

7. These remarks bring us to a fifth distinction ; by which 
propositions are divided into the categorical and the conditional. 
With Aristotle a categorical was simply an affirmative propo- 
sition ; but his disciple and successor, Theophrastus, gave the 
name to any statement, whether affirmative or negative, which 
is made unconditionally, or rather without any expressed con- 
dition. All subsequent writers follow Theophrastus in this 
use of language. They also oppose to the categorical the 
" conditional " proposition ; the condition here referred to 
being not an actual, but a supposed, condition. By a con- 
ditional proposition, therefore, we are to understand an asser- 
tion expressly depending on some hypothesis, or supposition, this 
dependence being indicated by "if," or so?ne other word intro- 
ducing the supposition. " If iron is heated, it will expand ; if 
a man is wounded, he may die," are conditional assertions. 
So also is the statement, " A whole number is either odd or 
even"; for this expresses conditions by "either" and "or." 

" Iron is a metal ; birds are oviparous ; food is necessary to 
life ; twice three are six ; all men are mortal ; some snakes 
are venomous ; an equilateral triangle must be equiangular ; 






86 THE MOBALIST. [Chap. X. 

a straight line can be drawn from one point to another in a 
plane ; France is a republic ; Carnot is president/' — these are 
categorical propositions. 

But while logicians rightly distinguish categorical and con- 
ditional statements, many overlook the fact that this division 
pertains to verbal, and not to mental, propositions. The dis- 
tinction is commonly presented as if it gave not merely the 
superficial form, but also the deeper nature of our thought. 
That a more profound discrimination is needed should be evi- 
dent to those who know that conditional statements can be 
changed to a categorical form, and that categorical statements 
can often be turned into conditionals. This latter is always 
and especially the case when the categorical assertion sets 
forth a general truth. 

Instead of saying, "If iron is heated, it will expand," we 
can say, " Heated iron expands " ; while the sentence, " A 
wounded man may die," is equivalent to, " If a man is wounded, 
he may die." Even the disjunctive conditional can be ex- 
pressed categorically ; though not by one proposition, it being 
a complex of assertions. For example, the four conditionals 
which compose the assertion, "A number is either odd or 
even," may be replaced by the following categoricals : " A 
number not odd is even ; a number not even is odd ; an odd 
number is not even ; and an even number is not odd." 

Conversely, all the categorical examples given above, except 
the last two (concerning France and Carnot), may be changed 
into conditionals ; thus, " If a mineral be iron, it is a metal ; 
if an animal be a bird, it is oviparous ; there must be food, if 
we would live ; if one doubles three, he has six ; if a being is 
human, he is mortal ; if a man is a scholar, he may be wise ; 
if the creature be a snake, it may be venomous ; if there be an 
equilateral triangle, it must be equiangular ; if two points be 
assumed in a plane, they can be connected by a straight line 
lying in that plane." Not only may many categoricals be thus 
changed into conditionals, but their true and internal nature is 
more fully set forth by the conditional than by their own form 
of expression. In short, while conditionals need no interpre- 
tation, categoricals are very often secondary modes of state- 



Chap. X.] PB0P0SP1T0NS AND PREDICATIONS. 8T 

merit which, are unconditional only in their verbal, and not in 
their mental, significance. 

8. Let us now close with a distinction which applies the 
same thought to propositions, or assertions, in their inner 
nature, which the distinction of categorical and conditional 
applies to their superficial character. In the fifth place, we 
say that propositions are either actualistic or hypothetical. 
Here, as the word " conditional " is used to designate proposi- 
tions hypothetical in form, we take the liberty to apply the 
term " hypothetical " to all propositions which are hypotheti- 
cal in their true character, whether they be expressed in hypo- 
thetical language or not. The peculiarity of such predications 
is, that they do not assume the reality of their antecedents or 
subjects ; and therefore also do not assert reality for their con- 
sequents or predicates. It is an hypothetical statement to say, 
" If a farmer be diligent, he will prosper " ; and to assert, in 
the general, "The diligent farmer will prosper," is equally 
hypothetical. For this last, although referring to the fact that 
some farmers are diligent, is not intended to assert fact, but 
only to affirm that, if a certain antecedent should exist, a cer- 
tain consequent will exist also. But to say regarding some 
known individual, " That honest and diligent farmer will 
prosper/ 7 would be actualistic. Propositions " conditional " in 
their verbal character are always hypothetical mentally, and 
therefore need no interpretation ; but, as we have already seen,, 
very many categorical statements are essentially hypothetical. 

Actualistic propositions are those which express belief in 
fact; that is, in the actual existence, or non-existence, of a 
thing. They do not always assert reality simply, or purely, 
as when one might say, " God created the world " ; they may 
set forth fact as necessary, or they may present something as 
probably, or possibly, a fact. 

All presentential assertions are actualistic, but inherential 
propositions have this character only when they assume the 
real existence of their subjects and express some conviction, 
great or small, qualified or unqualified, regarding their predi- 
cates. " There is bread in the cupboard ; there is no money 
in the house ; there may be flour in the barrel ; the judge is 



88 THE MODALIST. [Chap. X. 

impartial ; the witness may be mistaken ; that prisoner cannot 
be guilty ; he must be innocent," are actualistic assertions. 

The verbal form, or superficial significance, in designation 
of which the name " categorical " is given to ordinary propo- 
sitions, primarily pertains to actualistic conviction. That 
independent mention of the subject with which it begins 
naturally appears to present the subject as actually existent. 
This circumstance obscures the fact that the majority of cate- 
goricals are essentially hypothetical. 

The true state of the case, also, is further obscured, because 
the categorical form of statement, even when used hypotheti- 
cally, does not wholly lose its original force. In saying, "War 
is an evil," we refer to wars and their evils as realities even 
while our mental aim is not to set forth these things as facts, 
but to state the law — or general sequence — that if, or when- 
ever, there may be a war, it is an evil. The actualistic impli- 
cation in such a general statement is no essential part of it, 
but merely a concomitant of it. 

In addition to these natural causes of mistake logicians, by 
a defective use of terms, have positively inculcated the error 
of denying the hypothetical character to every categorical 
statement. Eor they have confined the name " hypothetical " 
to " conditional " propositions ; while that extensive class of 
assertions which are mentally hypothetical, but which may be 
either of the conditional or of the categorical form, has been 
left without designation, and almost without recognition. 
Let us remember that a proposition categorical in form may 
be hypothetical in its inner meaning. 



Chap. XL] CATEGORICAL PREDICATIONS. 89 



CHAPTER XL 

CATEGORICAL PREDICATIONS. 

1. Verbally free from hypothesis. 2. The predication-proper analyzed. 
The common, and the true, doctrine of the " copula." 3. Origin of the verb 
"to be" as copula. 4. Categorical assertions are simple or compound; 
5. Substantal or ascriptional ; 6. Affirmative or negative ; 7. Universal 
or particular. ' ' Distributed ' ' and ' ' undistributed ' ' terms. 8. Indefinite, 
and singular, propositions. 9. Hamilton's quantification of the predicate. 
10. Definitions, divisions, and " exclusive " predications. 11. The "pure," 
and the "modal," categoricals. 

1. Conditional propositions are simply hypothetical state- 
ments fully expressed : they will be further considered here- 
after. Categorical propositions are statements which are free 
from any expression of hypothesis : they are actualistic in 
form, though often hypothetical in fact. The principal varie- 
ties of categorical assertion constitute an important topic of 
study. Before discussing them, let us consider a part, or ele- 
ment, which is essential to every inherential proposition ; and 
which logicians call the " copula." 

2. Every predication-proper comprises, first, the subject 
about which the assertion is made ; secondly, the predicate 
asserted of the subject ; and thirdly, the copula, which is the 
verb "to be," expressed or understood, and agreeing grammati- 
cally with the subject. In saying, "The daffodil is a flower; 
the daffodil is yellow," the copula is expressed: in saying, 
" The daffodil blooms," it is understood, or rather it is united 
with the predicate and concealed in it. For this last sentence 
means, " The daffodil is blooming." 

The name "copula" is connected with the view that the verb 
" to be " in predications-proper indicates, not the existence of 
anything, but the union in thought of the predicate with the 
subject ; this conjunction of things being considered the es- 



90 THE MODALIST. [Chap. XI. 

sence of affirmation. Moreover, since the days of Aristotle, it 
has been held that the word " not," added to the copula so as 
to signify negation, indicates the mental separation of the 
predicate from the subject. 

These teachings are erroneous except so far as they imply 
that the copula expresses the essential, or differential, part of 
assertion. Affirmation is not a uniting, nor is negation a sep- 
t arating, of things in thought. The true doctrine is that affir- 
mation sets forth the existence, and negation the non-existence, 
of the predicate-object. In presentential assertion affirmation 
and negation take place simply upon the conception of the 
subject as existing and as non-existent, and without any join- 
ing or sundering of things. 

As to the " conjunction and separation " of things in predi- 
cations-proper, we have three remarks to make. First, compo- 
sition, or synthesis, is not especially necessary for affirmation, 
but is the condition of any predication whatever. For a predi- 
cate must be conceived of as related to a subject before it can 
be either affirmed or denied with respect to that subject. In 
affirming, "The candle burns," an action, conceived of in an 
appropriate relation, is asserted to exist in that relation; in 
the statement, " The candle does not burn," precisely the same 
thought-combination of entities is used, though it is accompa- 
nied by the assertion of non-existence. Secondly, negation, 
even when completed, does not involve any separation of 
things in thought ; though it may be naturally followed by the 
dismissal from our minds of the rejected predicate. To assert 
the non-existence of a thing which has been conceived of as in 
some relation is no more a mental sundering than the extinc- 
tion of a flame is the removing of it from the candle. The 
flame is not taken away ; it is extinguished where it is. So 
the predicate is not removed in thought, but is simply asserted 
not to exist. Finally, the assertion of separation, so far from 
being a negation, is only a specific case of affirmation. To 
exist in separation is incompatible with that kind of union of 
which we ordinarily conceive, and may be used to deny such a 
union ; but it is itself expressed by a combination of the pred- 
icate with the subject ; for this may be based on any relation 



Chap. XL] CATEGORICAL PREDICATIONS. 91 

whatever. Moreover, as it positively asserts separation, it 
implies the existence of both the things separated. To say, 
" The horse is free from disease," taken literally, implies that 
both horse and disease exist in separation from each other. 
But as the real point to be asserted is merely the non-existence 
of disease in the horse, and as this would follow if the disease 
were at a distance, the affirmation of the separation is used 
figuratively, and merely denies the existence of the disease. 
In such a case there is no real assertion of separation at all. 

We repeat, therefore, that the function of the verb " to be," 
alone in affirmations, and accompanied by " not " in negations, 4- 
is always to set forth existence and non-existence ; and that, in 
predications-proper, this function is conditioned on the union 
of things in thought. The mental separation of things — the 
conceiving of them as apart — is only indirectly and acciden- 
tally connected with negation. 

3. Here the question may be asked, How is it that the verb 
"to be" sets forth the existence of the predicate, when it agrees 
grammatically with the subject? This singular mode of speech 
must have originated in the days when men first began to 
make assertions. It seems to be a linguistic device in the use 
of which certain verbs, which were primarily used to indicate 
the existence of subjects, had predicate-facts attached to them 
by way of grammatical limitation. The different parts of the 
verb " to be " in our own language, and of corresponding verbs 
in other languages, are traceable to roots signifying to breathe, y* 
to live, to stand, to remain, to grow, to be born. In short, 
existence, originally, was expressed by words which signified 
more than mere existence. For example, men said, " The man 
breathes ; the man lives," meaning only, " The man exists." 
Then it was found easy and natural to express predicate-facts 
by adding something to the same verbs which had been se- 
lected to indicate the existence of the subject. It was said, 
" The man breathes free ; lives virtuous ; remains at home ; is 
born rational ; has grown wise ; has stood firm," the point of 
assertion being only, " The man is free ; is virtuous ; is at 
home " ; and so on. In like manner, negation was expressed 
by giving each verb a negative limitation; as, "The man 



92 THE 3I0DALIST. [Chap. XI. 

breathes not free ; lives not wise ; remains not at home." In 
the course of time the connecting verbs, entirely losing their 
proper significance, indicated only the existence (and the non- 
existence) of the predicate. 

In concluding our remarks concerning the copula, we must 
add, what is allowed by all, that the reference to time, ex- 
pressed by the different tenses of the verb, is no part of the 
copula, but must be attached either to the subject or to the 
predicate, as the analysis of the sentence may require. 

4. Let us now consider the leading varieties of categorical 
assertion, following, as in previous discussions, the method of 
logical division. First, categorical statements are either sim- 
ple or compound. The simple categorical has only one subject 
and one predicate; the compound is a condensed expression 
for several simple assertions, which are independent of each 
other yet have a common subject or predicate. "Caesar came 
and saw and conquered " is equivalent to " Caesar came ; Cae- 
sar saw; and Caesar conquered." "Caesar, Charlemagne, and 
Napoleon were conquerors " means, " Caesar was a conqueror ; 
Charlemagne was a conqueror; and Napoleon was a con- 
queror." The rules of logic pertain immediately to the 
simple categorical, and therefore presuppose a resolution of 
compound propositions into their components. 

5. In the second place, categorical assertions are either sub- 
stantal or ascriptional. This distinction concerns only the 
verbal form of predicates. The subject of every proposition is 
a substantal notion ; but a substantal assertion depends upon 
a substantal predicate. " Man is rational ; the gentleman lives 
near me," are ascriptional propositions : " Man is a rational 
being; the gentleman is my neighbor," are substantal predi- 
cations. Evidently this distinction pertains to superficial 
thought ; because any ascriptional statement may be replaced 
by a substantal equivalent ; and because this process may be 
reversed. We make such changes almost unconsciously in our 
ordinary reasonings. For instance, the substantialization of 
the predicate occurs whenever we " convert " an ascriptional 
proposition in order to show what it authorizes us to say 
regarding the predicate considered as the subject of an asser- 



Chap. XL] CATEGORICAL PREDICATIONS. 93 

tion. For ascriptional statements are convertible only after 
being changed into the snbstantal. Therefore, replacing "No 
men are perfect/' by " No men are perfect beings," we convert 
and say, " No perfect beings are men." 

Because every ascriptional proposition may be given sub- 
stantal form, and for some uses must assume this form, it has 
been taught that all propositions, when fully expressed, are 
substantal : in other words, that every predication is essen- 
tially the affirmation or denial of identity. This is an extreme 
opinion. It is not sustained by the analysis of mental facts. 

6. With respect to "quality," or " assertivity," categorical 
predication is either affirmative or negative. This distinction, 
being connected with the essential nature of propositions, has 
been discussed already. 

7. We proceed, therefore, to that distinction which per- 
tains to the " quantity " of propositions and which separates 
them into the universal and the particular ; for this division is 
important only as applied to categorical assertions. " Quan- 
tity " is the extent of the applicability of a proposition ; and it 
is of two kinds, according as the subject-notion indicates a 
whole class of things or only part of a class. In the former 
case the subject is said to be "distributed," and the propo- 
sition is "universal"; in the latter case the subject is "undis- 
tributed," and the proposition is " particular." " All men are 
mortal," is an universal proposition ; " Some men are wise," 
is a particular one. 

The term " distributed " might designate the conception of 
any number of things conceived of as individuals, and not 
collectively. In saying, " All men are the family of Adam," 
the expression "All men" is used collectively; but in, "All 
men are mortal," it is used distributively. And if we should 
say, " One man could not lift a ton, but some — or several — 
men could," the word "some" would have a collective force; 
but in, " Some men are learned," its force is distributive. 
Therefore, in a broad sense, not only the word "all," but also 
the word " some," may be used distributively. In logic, how- 
ever, a term is not called distributed unless it be distributed 
fully, or used in its widest possible application ; and a term, 



94 THE MODALIST. [Chap. XI. 

though conceived distributively, is yet considered undistri- 
buted if it be applied to anything less than the whole class. 
Hence the rule that universal propositions distribute the sub- 
ject, while particular propositions do not. 

8. Under the head of quantity, besides the universal and 
the particular, Aristotle mentions the indefinite proposition, 
and the singular. These, however, should not be treated as 
separate species. Quantity is indefinite when it is either not 
determined in thought or not expressed in language : in the 
latter case it is also styled " indesignate." " Gold is metallic ; 
horses are used for riding," are of indefinite quantity, but a 
little thought makes one of these universal and the other par- 
ticular. The quantity of a predication can always be deter- 
mined ; it is universal if we know that the predicate belongs 
to the subject as distributed, and particular if we cannot say 
so. For the quantity of an assertion is based on what we are 
able to say. 

A singular proposition is one with a singular subject. It 
makes an assertion about one object conceived of with its 
individual peculiarities, or about more than one object thus 
conceived of. For example, " The Gracchi were the head of 
the agrarian party." Logicians class the singular with the 
universal proposition ; as its assertion pertains to every indi- 
vidual mentioned, whether one or more. This view may be 
accepted, if singular predications be allowed quantity at all. 
But the truth is that the " quantity " discussed in logic serves 
a special purpose as related to general, or generic, classes of 
things, but has no proper significance in connection with 
singular assertions. 

The quantity of a proposition may be given either a united 
or a plural expression. Instead of, " All men are mortal," we 
can say, " Every man," or "any man," or "man always," is 
mortal. Instead of, "Some serpents are venomous," we can 
say, "Sometimes a serpent is venomous." 

The expression of quantity is also often connected with that of 
quality. In universal negatives the adjective "no" indicates 
both these elements of the predication. Thus we say, " No 
men are perfect" ; which is probably a contraction for, "There 



Chap. XL] CATEGORICAL PREDICATIONS. 95 

are no men who are perfect." Occasionally, too, the particle 
" not " qualifies the quantity, and not the main matter, of the 
assertion. When we say, " All men are not wise," or, " Every 
man is not wise" ("all" and "every" being the emphatic 
words), we do not make universal predications, but mean, first, 
that some men are, or may be, wise, and secondly, that the 
men who are wise are not all. These modes of speech are 
based on the fact that the quantification of the subject is 
really a kind of predication which modifies that predication 
of which logicians speak ; and they illustrate the general prin- 
ciple that the verbal proposition is often indirect in the expres- 
sion of thought, and may need " interpretation." 

9. Sir William Hamilton maintained that the predicate, as 
well as the subject, is quantified in every proposition. "The 
subject and the predicate," he says, "have each their quantity 
in thought. This quantity is not always expressed in lan- 
guage, for language tends to abbreviation ; but it is always 
understood." On the basis of this doctrine and others con- 
nected with it, — as, for example, that a proposition is an 
equation, or an identification, of two notions, — Hamilton re- 
constructed all the formulas of reasoning. 

The insuperable objection to Hamilton's doctrine is that it 
is not in accord with fact. It is not true that every predicate 
is quantified in thought. In ordinary categorical assertions 
the subject-notion is conceived as applicable either to all or 
to some of a logical class ; in other words, is quantified ; but 
the predicate simply characterizes the subject. When we say, 
"Birds are feathered; fishes live in the water; no metal is 
a vegetable ; some men are trustworthy," we characterize the 
subject positively or negatively. It is no part of our thought 
that all feathered animals are birds ; that only some things 
which live in the water are fish ; that no vegetable is metal ; 
and that no trustworthy beings are some men. The most that 
can be allowed is that the predicate is quantifiable. By re- 
flecting on the nature of the assertion we can tell whether it 
gives information respecting the whole class which the predi- 
cate may name or respecting only a part of it. In the former 
case the predicate may be distributed ; in the latter it is undis- 



4 



96 THE MODALIST. [Chap. XI. 

tributed. But this quantification is no part of ordinary asser- 
tion ; it is only an addition which may be made to it. 

This is evident even in cases where the quantification of the 
predicate may easily take place ; as, for example, in assertions 
which apply to all the members of a class and to them only. 
When we say, " All equilateral triangles are equiangular tri- 
angles," a little reflection on the relations of the things men- 
tioned enables' us to distribute the predicate, so as to say, 
conversely, "All equiangular triangles are equilateral." But 
if we did not reflect on the peculiarity of the case as affecting 
the predicate, the first proposition would merely signify that 
"Every equilateral triangle is equiangular." On the other 
hand, when we say, "Every equilateral triangle is half the 
rectangle formed by one of its sides and the perpendicular let 
fall on that side from the opposite angle," still more consider- 
ation is needed to perceive that this proposition does not war- 
rant the converse, that " Every triangle which is equal to half 
the rectangle formed by base and perpendicular is equilateral." 

10. Some teach that definitions always distribute their 
predicates, and that when we say, " Man is the rational ani- 
mal," we mean, " All men are all the rational animals." But 
this is an extreme view. The object of definition is simply to 
characterize the subject definitely; which can be done without 
distribution of the predicate. Even the exact identification 
of the subject with the predicate belongs to the verbal form, 
rather than to the essential nature, of definition. 

The only propositions which actually quantify the predicate 
are those which are intended to make assertions respecting the 
complete or the partial identity of classes. Such, especially, 
are those enumerations which identify a genus with some or 
all of its specific kinds. The predicate is distributed in say- 
ing, " Fishes, birds, reptiles, and mammals are the vertebrates " ;. 
it is undistributed in the statement, " The horse, the dog, the 
lion, and the tiger are some of the quadrupeds." As compari- 
son of classes may take place in connection with any general 
statement, the predicate may always be quantified ; but such 
comparisons occur only occasionally. 

Here, however, " exclusive," or " exceptive," predications 



Chap. XL] CATEGORICAL PREDICATIONS. 97 

should be mentioned, for they so qualify the subject as espe- 
cially to suggest the distribution of the predicate. "Only 
men philosophize," or, "None but men philosophize," immedi- 
ately suggests that all who philosophize are men. This mode 
of predication is really compound. The above example pri- 
marily asserts, first, that men philosophize, and secondly, that 
no other earthly beings do. But as our interest concerns those 
who philosophize and not the rest of the world, the inference 
arises unbidden that men — that is, some men — are all the 
philosophers ; or that all philosophers are men. 

Ordinarily the quantification of the predicate is not imme- 
diately suggested by the nature of the assertion, but is a 
special addition which prepares the original statement for the 
process called " conversion." 

11. One other distinction between categorical propositions 
remains to be considered. It divides them into the pure and 
the modal. This classification was fundamental with Aristotle, 
and occupies a larger place in his system than the quantifica- 
tion of the predicate does in that of Sir William Hamilton ; 
but it has been rejected by almost all logicians. It will be the 
first topic of our next discussion. 



98 THE MODALIST. [Chap. XII. 



CHAPTER XII. 

THE ILLATIVE. PROPOSITION. 

1. "Pure" categoricals might be styled "dogmatic." Verbally, they 
are assertions " de inesse " ; and do not express logical sequence. 2. " Mo- 
dal" categoricals are expressly either apodeictic or problematic. 3. Neces- 
sity, impossibility, possibility, and probability, as related to one another. 
4. Logical necessity and possibility distinguished from causal. 5. Aris- 
totle's modals wrongly rejected. 6. The distinction between "pure" and 
"modal" is verbal and superficial. 7. In addition to the six generic 
distinctions already made, propositions are (a) factual, or historical, and 
(6) illative, or inferential. 8. The illative assertion may be uncontracted 
in form ; or contracted and categorical. 9. Except for usage, we might 
speak of "actualistic conditionals." 10. All inference may be expressed 
by two propositions. 11. Dogmatic propositions do not explain modal, 
but the modal the dogmatic. 

1. A categorical proposition is "pure" when, so far as 
verbal thought is concerned, it asserts the inherence or the 
non-inherence of the predicate simply as fact or truth. In 
other words, a pure categorical merely states that the predi- 
cate does, or does not, exist in its relation to the subject. 
" Arsenic is poisonous ; some metals are not heavy," are pure 
categoricals, or assertions " de inesse " : the first sets forth the 
existence of the quality " poisonous " in arsenic, the second 
the non-existence of " heavy " in some metals. 

The term " pure " designates this class of propositions very 
inadequately. On this account, probably, Kant distinguishes 
them as "assertory." But all predications assert; the pecu- 
liarity of these is only that they assert simply, or without 
reference to any ground, or reason. A more distinctive desig- 
nation is desirable : we may, therefore, sometimes style pure 
categoricals " dogmatic " statements, or dogmas ; because, so 
far as verbal expression goes, they set forth matters of knowl- 
edge, or of belief, in a simple and unqualified way. The 



Chap. XII. ] THE ILLATIVE PROPOSITION. 99 

assertions, " Gold is valuable ; savages are treacherous ; all 
metals are minerals ; some minerals are metals," may be styled 
dogmatic, because, in their simple positiveness, they resemble 
doctrinal statements, such as that G-od is merciful ; that Jesus 
Christ died for sinners ; and that the present life is one of 
probation for a future state of existence. 

2. On the other hand, "modal" categoricals expressly present 
the existence or the non-existence of the predicate as in some 
way logically connected with, or consequent upon, the existence of the 
subject. They are of two principal kinds ; the apodeictic, which 
predicates a thing either as necessary or as impossible ; and 
the problematic, which predicates a thing either as possible, or 
as probable. The apodeictic has also been called the demon- 
strative, and the problematic, the contingent. " An unsupported 
weight must fall ; animals cannot live without air," are apo- 
deictic propositions ; and two more such are contained in the 
sentence, "Straight lines parallel for any distance cannot 
meet however prolonged, but must continue parallel." " The 
straying horse may have taken any one of a number of roads," 
is a problematic categorical asserting possibility. "He has 
probably taken that leading to his former home," is a propo- 
sition of the same general class in which probability is 
asserted. 

We must note that necessity, impossibility, possibility, and 
probability enter as elements into modal assertion only because 
they indicate different modes in which the predicate may be logically 
connected with the subject, and therefore, also, different forms and 
degrees of conviction regarding the predicate. To assert any 
one of these logical relations simply as a fact and for its own 
sake, and not as the ground for believing in something as 
necessary or possible or probable, would not be a modal predi- 
cation. The statement that " proficiency in science is possible 
for any young American who avails himself of all his advan- 
tages" would be pure, not modal, were the design of the 
speaker simply to set forth the fact of the possibility. But 
should one say, "A young American who has used all his 
educational advantages may be — or is possibly — proficient in 
science," this would be a modal proposition; the possibility 



100 THE MODALIST. [Chap. XII. 

mentioned in it would be asserted, not for its own sake, but to 
indicate the basis and the character of a judgment. 

3. Of the four modes of logical connection necessity and 
possibility are philosophically prior to the other two. Im- 
possibility and necessity both relate to precisely the same 
state of things and differ only because of a difference in our 
modes of regarding things. Whenever anything is a fact, and 
no power can make it otherwise, it is necessary ; and when- 
ever anything is not a fact, and no power can make it a fact, 
it is impossible. But as, whenever anything is fact we can 
conceive also of that which is not fact corresponding to it,, 
necessity and impossibility may always be asserted together. 
If it is necessary that something should be, it is impossible 
that it should not be ; and if it is necessary that something 
should not be, it is impossible that it should be. Necessity is 
called positive or negative according as the fact to which it 
pertains is one of existence or of non-existence ; and impossi- 
bility is characterized in the same way as belonging to that of 
which we conceive as the opposite of fact. Since impossibility 
thus originates from the same conditions with necessity, and 
is, as it were, the other side of the same thing, an under- 
standing of necessity reveals the nature of impossibility, also. 

Probability, likewise, is conditioned on possibility; yet not 
so simply and directly as impossibility is conditioned on neces- 
sity. When out of a number of possible alternatives one, 
and only one, must be true, and we have no reason to expect 
one more than another, we say that they are equally likely, or 
probable. But if a given proportion of those equal individual 
possibilities have a general character which may be realized 
in one and the same event, then that event is probable accord- 
ing to the ratio of the chances, or possibilities, for it, as com- 
pared with the total number of chances. Thus probability 
results from a general necessity combining with one or more 
individual possibilities of a given character. If a lottery con- 
tain ten blanks and two prizes, the drawing being settled as 
certain, the probability of any individual possibility is one- 
twelfth, and that of any given ticket gaining a prize is two- 
twelfths, or one-sixth. The connection of probability with 



Chap. XII. ] THE ILLATIVE PROPOSITION. 101 

possibility is indicated by the use of the same auxiliary verb, 
" may," to express either of these conceptions. 

4. Logical necessity and possibility are of a very general 
character, and do not pertain only to effects as related to their 
causes. Therefore they must not be confounded with causal 
necessity and possibility. The latter are only specific modes 
of the former ; for things may be possible or necessary with- 
out any reference to causation. It is possible that a pint of 
fluid should be contained in a quart measure ; and it is neces- 
sary that the fluid which fills two pint measures should be 
equal to that which fills the quart measure. So, also, if an 
exterior angle be formed by prolonging one side of a plane 
triangle, it may be twice as large as one of the interior and 
opposite angles, and must be equal to both those angles taken 
together. In these cases necessity and possibility arise from 
arithmetical and geometrical, not from causational, relations. 

5. The only modal propositions of which Aristotle treats 
are those which assert either necessity or impossibility or con- 
tingency ; under which last head both possibility and proba- 
bility are included. The Greek commentators on Aristotle, 
however, misapprehending his conception, enlarged the sphere 
of modality by making it embrace every proposition the pred- 
icate of which has an adverbial addition. According to them,. 
" Alexander conquered Darius honorably," would be a modal. 
But this proposition differs only in expression from the more- 
direct statement, " Alexander's conquest of Darius was honor- 
able." Then subsequent logicians, perceiving that such adver- 
bial propositions are in reality pure categoricals, concluded 
that a modal proposition is merely a pure proposition irregu- 
larly expressed. They were the readier for this doctrine, 
because Aristotle's discussions of those forms of argument in 
which modal thought is recognized, are marvellously complex 

% and difficult. Thus it has come to pass that, at the present 
day, modal predication is barely mentioned by logicians, and 
is then immediately dismissed as of no scientific importance. 
"The whole doctrine of modality," says Professor Francis 
Bowen, " is now rightfully banished from pure logic." 

But it is a mistake to suppose that modal does not differ 



102 THE MODALIST. [Chap. XII. 

seriously from pure predication, or that the necessity and con- 
tingency which it asserts are simply parts of the ordinary 
predicate. The modality, like the "quantity," of assertions 
should be regarded as a sort of added predication of which the 
main body of the assertion is the subject; and which is in- 
tended to qualify and complete the assertion. As " all " and 
"some" do not modify our conception of the subject of a 
proposition, but only show whether the statement is univer- 
sally or partially true of a class of things, so " must " and 
"may" do not modify our conception of the predicate, but 
only indicate whether the assertion is based on a necessary or 
on a contingent connection of the predicate with the subject. 
This is apparent when, instead of saying that, " Such a thing is 
necessarily or possibly or probably so and so," we say, " It is 
necessary or possible or probable that such a thing is so and 
so " j for, in this latter form of statement, the modal words 
evidently do not qualify the predicate, but only tell how the 
predicate is logically connected with the subject. Moreover, 
as all inference arises from perceiving the connection of things 
with each other, it seems unwise to deny the importance of 
modal assertions. 

6. In order to understand the true significance of this class 
of predications, and of categorical propositions in general, it 
is necessary to note that the distinction between " pure " and 
u modal," like that between conditional and categorical propo- 
sitions, is really of a verbal and superficial character, and must 
be supplemented by another distinction which relates to the 
essence of thought. For that logical connection which modal 
assertions express is often indicated by implication in pure 
categoricals, so that, were we to think of propositions only in 
their mental character, we must allow that many pure categori- 
cals are of a modal nature. It is especially true that when a 
pure categorical embodies a general principle, it is modal in its 
inner meaning. Indeed, as a rule, pure universal statements 
are apodeictic in their force, and set forth necessary truths ; 
while pure particular statements are problematic, and present 
principles of contingent belief. The assertions, "All men are 
mortal ; no men are perfect ; some merchants are successful ; 



Chap. XII. ] THE ILLATIVE PROPOSITION. 103 

some savages are not treacherous," when employed as premises 
in argument, signify that man must die; that man cannot reach 
perfection; that a merchant may be successful; and that a savage 
may not be treacherous. 

7. The distinction pertaining to internal and mental prop- 
ositions, to which we are thus brought, relates not only to 
those expressed in categorical form, but to all propositions 
whatever. It divides assertions into the factual, or historical, 
and the illative, or inferential. A factual proposition is one 
which asserts mentally what the pure or dogmatic proposition 
sets forth verbally, namely, some fact of existence or of non- 
existence, simply as such. " Csesar conquered the Gauls ; the 
Hindoos are Asiatics; Kome is in Italy; Locke was born in 
1632," are statements of this character. On the other hand, 
any proposition which asserts something as a logical conse- 
quence, either expressly or by implication, may be distin- 
guished as illative, or inferential. Factual assertions form 
the body of history or narration ; illative constitute the most "X 
important part of philosophical knowledge and theory. Both 
are radical modes of rational thought ; yet, of necessity, the 
enquiries of the logician have much more to do with illative 
than with factual statements. 

8. To understand the scope of this fundamental distinction 
between modes of assertion we need not dwell longer on factual 
propositions ; but a subdivision of illative predications seems 
necessary. For, in addition to the categorical method of indi- 
cating illation, which may be distinguished as the secondary, or 
shortened, mode (and which is of two species, the modal, and 
the pure, or the dogmatic), there is the primary and uncontracted 
method, one form of which has already been considered in the 
" conditional " proposition. For the conditional proposition is 
of a two-fold nature ; it is not only suppositive, or hypotheti- 
cal, but also illative, or inferential. This latter character is 
sometimes indicated by the word " then " introducing the con- 
sequent : instead of saying, " If the man be honest, he will pros- 
per," we say, " If the man be honest, then he will prosper." 

9. It is because of this inferential force that fully expressed 
hypothetical propositions have been styled "conditionals." 



4- 



104 THE MODALIST. [Chap. XII. 

For a condition is not necessarily a thing supposed. Ordina- 
rily it is that which is requisite to the existence of anything. 
In the present connection it signifies the reason, or logical 
antecedent, of some consequent. For this always either is, or 
contains, the only condition requisite for the existence of the 
consequent. Other conditions than the one contained in the 
antecedent may be requisite, and often are, but in that case 
these are assumed as already existing, so that the consequent 
depends on that one condition only, and must follow if that 
condition be a reality. In order that the man may prosper, 
other things than honesty may be needful; these, however, 
are known or assumed when we say, " If the man be honest, 
he will prosper." But evidently a logical antecedent with its 
necessitant condition, no less than the ordinary and merely 
necessary condition, may be either real or supposed. There- 
fore the restriction of the term " conditional " to hypothetical 
statements is somewhat arbitrary. 

Therefore, also, we say that there is another primary expres- 
sion of illation, which, were it not for fixed usage, might be 
called a conditional proposition. We refer to actualistic asser- 
tion when it is made on the strength of some given reason. For 
example, " Since the man is honest, he will prosper ; because 
the night has been clear, there must be dew on the grass ; the 
triangle is equilateral, for it is equiangular," might be styled 
actualistic conditionals. But, because their conditions, or ante- 
cedents, are not suppositions, but realities, we must call them 
uncontracted actualistic illatives. 

The question may be raised whether an uncontracted state- 
ment of illation can properly be called a proposition, inasmuch 
as it contains two propositions, one of which is inferred from 
the other. This question relates both to "conditional" prop- 
ositions, and to those actualistic assertions just considered. 
We reply that these uncontracted statements may be styled 
either inferences or propositions according to the manner in 
which we view them. If our interest be chiefly directed to the 
thing inferred, then the consequent assertion together with the ante- 
cedent as a kind of prefix, is called a proposition; but if our scru- 
tiny regard antecedent and consequent alike, then we speak of 



Chap. XII. ] THE ILLATIVE PROPOSITION. 105 

an inference. At the same time it may be allowed that any 
uncontracted statement of an inference contains mnch more 
than a mere proposition, and receives this name. only through 
a secondary use of language. On the other hand, the illative 
categorical, whether modal or dogmatic, is rightly called a 
proposition, because, so far as verbal form is concerned, it is 
a single existential statement ; and because our language relates 
primarily to the verbal form. Mentally, every such proposition 
is an inference which has the subject of the categorical for its 
antecedent and the predicate for its consequent. 

10. In speaking of a certain style of proposition as the 
uncontracted expression of an inference, w r e do not mean that 
inferences are always expressed by it in the fullest possible 
way. Philosophical completeness often calls for developed 
forms of statement in which things are expressed which would 
otherwise be understood. We mean only that ordinarily and 
primarily an inference is stated by two propositions in the 
sequence of reason and consequent. 

Moreover, this binary combination of propositions can be so 
used as to state any inference completely ; and is the only form 
in which every inference may be completely stated. When 
the antecedent is a single truth or fact, the inference must be 
set forth by two propositions ; and when the antecedent is a 
combination of assertions, this combination must be regarded 
as one complex statement, to be followed by one other state- 
ment as its consequent. "If all men are mortals, then some 
mortals are men," is an inference which admits of only one 
premise ; while in the following inferences a plurality of prem- 
ises is expressed by one statement : " A is equal to B which is 
equal to C ; therefore A is equal to C. If A is older than B 
who is older than C, then A is older than C. Since A is a part 
of B which is a part of C, A is a part of C. Because Hindoos 
belong to the class Men who are mortal (or have the nature of 
man which necessitates mortality), Hindoos are mortal." All 
inference, therefore, may be expressed by one antecedent prop- 
osition and one consequent. This is as it should be ; for it is 
the essential nature of inference to assert a consequent 
because of a reason. 



106 THE MODALIST. [Chap. XII. 

11. Since the illative categorical proposition is a secondary 
and shortened form of statement, it evidently should be ex- 
plained by a reference to the primary and uncontracted in- 
ferential proposition. This, however, reverses the ordinary 
teaching of logicians. For, after entirely discarding modal 
predications, they explain "conditional" propositions as being 
of the same nature with pure categoricals ; and then base their 
theories of reasoning on the recognition of these last alone. 
The unsatisfactory character of this course is especially appar- 
ent when we see how artifice is often needful to give cate- 
gorical form to a conditional statement. Sometimes this is 
effected without difficulty; the assertion, "If iron is impure, it 
is brittle," is easily replaced by, " Impure iron is brittle." 
But artifice is often necessary ; as, for example, when recourse 
is had to the words "case of." Thus the conditional, "If 
Aristotle is right, slavery is a proper institution," is trans- 
muted into the categorical, " The case of Aristotle being right 
is the case of slavery being a proper institution." This state- 
ment is both less natural and less explicit than the original 
proposition. In particular the " case " might be a real instead 
of a supposed case, and instead of signifying, "If Aristotle is 
right," and so on, might signify, "Since Aristotle is right, 
slavery is a proper institution." 

It is frequently taught also that ,the conditional judgment, 
when transmuted, always gives rise to an universal categorical. 
This is a mistake resulting from the fact that most conditionals 
assert a necessary consequence. Cases of contingent sequence 
cannot be expressed by a pure universal proposition. " If iron 
be brittle, it may be impure," has for its modal equivalent, 
" Brittle iron may be impure," and for its dogmatic equivalent, 
" Some brittle iron — or brittle iron sometimes — is impure." 

The consideration of illative assertion concludes the second 
part of logic, which relates to propositions, or existential state- 
ments, as such ;. and it has had the effect of introducing us into 
the third part of logic, which concerns inference. This result 
has arisen from the duplex character, verbal and mental, which 
belongs to propositions as expressions of thought. Primarily 
propositions express assertion, simply, and not inference. 



Chap. XIII.] INFERENTIAL SEQUENCE. 107 



CHAPTER XIII. 

INFERENTIAL SEQUENCE. 

1. Inference defined. The law of Reason and Consequent. 2. Infer- 
ences are (a) single-grounded, double-grounded, or many-grounded ; 
(6) immediate or mediate ; (c) apodeictic or problematic. 3. The law of 
Conditions. 4. Necessary, or logical, relations. 5. A condition does not 
necessitate, but is necessitative. The exact necessitant, which reciprocates 
with its consequent. 6. Why the ordinary necessitant does not recipro- 
cate. 7. The inference of the necessary to be, and of the necessary not 
to be, or the impossible. 8. Possibility : its nature and modes ; the law 
of its inference. 9. The possible not to be ; how inferred. 10. Contin- 
gency. 11. Probability. 

1. Inference, or illation, is the process whereby we assert 
one thing to be fact or truth, because of its connection with 
some other thing, or things, which we assume to be true. 
The radical principle to which all inference conforms has been 
called the law of Antecedent and Consequent, or of Reason 
and Consequent, or of Sufficient Reason, or of Adequate Rea- 
son. This law simply generalizes the truth that two things, 
or facts, by reason of their respective natures, are often so 
connected with each other that the reality of the one may be 
the ground of our believing in the reality of the other. Infer- 
ence, therefore, takes place, not from the principle of Antece- 
dent and Consequent, but only according to it. In every case 
we think first of a reason and then of a consequent ; but the 
consequent is accepted because of its connection with the 
reason, and not because it is connected with the law of Reason 
and Consequent. So far from individual inferences depend- 
ing on a knowledge of this law, the knowledge of the law is 
derived from analyzing them. 

2. An inference, if based on a single fact or statement, may 
be called single-grounded ; if based on two statements it may 



108 THE MODALIST. [Chap. XIII. 

be styled double-grounded; and it may be distinguished as 
many-grounded, if based on three or more statements. But 
even though, there may be a plurality of premises, there is 
only one antecedent; and for the constitution of this the 
premises must be combined. 

Inferences are either immediate or mediate. In the former a 
consequent is inferred from an antecedent without any interven- 
ing link of illation. We assert that because A exists, C exists : 
we say, "Because this line is straight, it is the shortest possible 
between the terminal points." On the other hand, mediate in- 
ference arises when the consequent of a first inference is the 
antecedent of a second ; and it conforms to the law that the 
antecedent of a second antecedent is the antecedent also of the sec- 
ond consequent. Let B follow from A, and C from B ; then C 
follows from A. We say, " If he is human, he is rational, and 
if he is rational, he is responsible ; therefore if he is human, 
he is responsible." Such inference is mediate because a second 
inference intervenes between the first and the third ; . and yet 
more because, in the concluding inference, the antecedent of 
the first inference becomes connected with the consequent 
of the second through that common part which is consequent 
of the first and antecedent of the second. 

Mediate inference is often called reasoning, or ratiocination ; 
while the word " inference," when used alone, generally signi- 
fies immediate inference. In the remainder of the present 
chapter, using the term in this limited signification, we shall 
discuss immediate inference only. The consideration of this 
topic properly comes before that of reasoning. 

Viewed with reference to the mode of sequence between 
antecedent and consequent, inferences may be divided, as 
illative propositions have been, into the apodeictic and the prob- 
lematic. In the former of these consequents are inferred as 
necessary, or as impossible; in the latter as possible, or as 
probable. This distinction is sometimes expressed by saying 
that inferences are either necessary or contingent. In one 
sense, however, all correctly formed inferences are necessary ; 
for every just conclusion is necessary as a matter of belief, or 
conviction ; even though it may not be necessarily, but only 



Chap. XIII. ] INFERENTIAL SEQUENCE. 109 

possibly or probably, true. The principles of necessary con- 
viction may be either problematic or apodeictic, while those 
of necessary truth are apodeictic only. It is, however, most 
important to note that every mode of inference arises from a 
recognition by rational beings of the necessary relations of things. 

3. The significance of this statement will become apparent 
if we can perceive how the sequence of antecedent and con- 
sequent in its various forms is connected with an universal law 
of existence, namely, that all beings and natures exist under 
conditions, every nature having conditions of its oivn, and like 
natures having like conditions. This law, which, like that of 
reason and consequent, is the generalization of a necessity 
perceived in individual cases, may be styled the law of Con- 
ditions. It can be easily apprehended, provided only we 
carefully determine that conception which philosophy here 
attaches to the word "condition." 

This term, derived from "condere," to put together, or con- 
struct, first signified whatever may be connected with the 
formation, or constitution, of a thing; any prerequisite, or 
constituent, or concomitant ; then it was used, more widely, for 
whatever may attach itself in any way to the existence of a 
thing. Thus industry is a condition of success ; sanity and 
insanity are conditions of mental life ; the fulfilment of the 
terms of a contract is the condition of a claim to its benefits ; 
one's financial condition is the state in which he finds himself 
as related to pecuniary resources. 

In the loose general sense now described, conditions may be 
either contingent, and occasional, or necessary, and invariable. 
For, while industry is the indispensable condition of success, 
sanity is not inseparably connected with mental life ; and one 
who is now in a bad financial condition may be prosperous 
hereafter. Even the stipulation of a contract may be so 
changed or supplanted that the performance may be no longer 
required before the bestowment of the reward. Philosophy 
and logic, however, speak of those conditions only which are 
absolutely necessary to the existence of a thing ; therefore we 
now define a condition to be a second thing so related to a first 
that the first cannot exist without the second ; from which it 



110 THE MODALIST. [Chap. XIIL 

follows, also, that if the first thing exist, the second must exist 
along with the first. Space is a condition of motion ; because 
without space there could be no motion, and if there is motion 
there must be space. 

4. The relations connecting conditions with the things con- 
ditioned are of great variety. They pertain to objects as in 
space or in time, or as having number or quantity or size or 
shape, as being numerically the same or different, as being 
similar or dissimilar in nature, as being wholes and parts, or 
as being endowed with active and passive qualities and subject 
to the law of cause and effect. The metaphysician studies- 
such relations specifically ; logicians are concerned only with 
their general character as being necessarily connected with the 
conditioned object, and as necessitating the condition. 

In saying that the condition is necessitated by reason of its 
relation to the thing conditioned we refer to logical, and not 
to causational, sequence. In logic an effect may necessitate a 
cause as truly as a cause an effect. G-od, as eternal and self- 
existent, is free from causal conditions and causal necessity, 
but, as creator of the universe, He is logically necessitated. 
He is the only adequate, and, therefore, the necessary, cause 
of the universe. Then, as we have seen, necessity may arise 
from other relations than those of cause and effect. When 
we say, " What is part of a part is part of the whole," we do 
not present one fact as caused by another, but only as accom- 
panying that other in a way that no power could prevent or 
change. That general necessity of which logic speaks has an 
all-comprehensive sphere ; it is well described by Aristotle 
when he says that when a thing exists, and no power can make it 
not exist, it is necessary. Tor he thus teaches that necessity 
does not originate from power, but is the quality, or relation, 
which belongs to certain modes of existence as being beyond 
the operation of power. 

While a condition is necessitated by the thing conditioned,, 
and may be inferred from it as a consequent from an antece- 
dent, it is noticeable that we seldom regard the same thing as 
a consequent and as a condition For we speak of conditions 
when our enquiry concerns the thing conditioned, but of con- 



Chap. XIII.] INFERENTIAL SEQUENCE. Ill 

sequents when the question concerns the consequent itself. 
Consequents differ from ordinary conditions because they 
belong to that class of objects which secures our primary 
interest and attention ; and to which things which we conceive 
of as conditioned also belong. 

5. If things could be inferred from their conditions, as 
these may be inferred from the things conditioned, we would 
never be at a loss to find an antecedent for a consequent. 
Such is not the case. Nevertheless, while a condition ordina- 
Tily does not necessitate what it conditions, it has what may 
be called a contributory necessitative force, and by reason of 
this it may help to necessitate what it conditions. For exam- 
ple, a straight line is a condition of a plane triangle, and must 
exist if the triangle exist; but it does not necessitate the 
triangle. If, however, there be three straight lines of indefinite 
length in the same plane which do not cross one another at 
the same point, and no two of which are parallel to each other, 
there must be a triangle. Thus three or four conditions may 
so combine as to form an antecedent necessitating the thing 
conditioned. Such a combination of conditions is itself a 
compound condition ; it is both necessary as a condition and 
necessitating as an antecedent; therefore it may be styled a 
necessitant condition. 

Whenever an antecedent is thus a necessitant condition of 
its consequent, the inference admits of simple conversion. In 
other words, the consequent may be used as an antecedent, 
and the antecedent as consequent, in a new inference. For 
this reason, in reference to a four-sided rectilineal figure, we 
can say, not only, "If the opposite sides are parallel, the 
opposite angles are equal," but also, " If the opposite angles 
are equal, the opposite sides are parallel." And, if either of 
these things be not so, we can say that the other is not so too. 

6. Ordinarily, however, an antecedent is not simply a neces- 
sitant condition, but is something which contains such a condi- 
tion. Therefore most inferences do not admit of simple and 
thorough conversion. The logical rule is that we may assert 
the reason and then assert the consequent, and that we may 
deny the consequent and then deny the reason ; but that we 



112 THE MODALIST. [Chap. XIII. 

cannot either assert the consequent and then assert the reason, 
or deny the reason and then deny the consequent. The ground 
for this rule is that although the consequent cannot exist with- 
out such a necessitant condition as is contained in the antece- 
dent, such a condition may be contained in some other antece- 
dent ; and so the consequent may exist while that antecedent 
does not exist, and that antecedent may be non-existent while 
yet the consequent is a fact. 

The nature of a necessitant condition may be illustrated by 
that of the exact philosophical cause of an effect. Sometimes 
we say that the same effect may be produced by a variety of 
causes ; and this is true. One may become warm by exercise, 
or with a fire, or by putting on heavy clothing. Yet there is 
a common heart, or core, in each of these methods, on which 
its efficiency depends : in each case the heat arises from the 
collection of a certain amount of chemical, or molecular, action 
upon or within one's body. So, also, the general cause of 
disease is the partial failure of some bodily function ; and this 
failure may take place in a variety of ways. The general 
cause of motion is the uncounteracted application of force; 
but force may be either attractive or repulsive, and may be 
exerted by either animate or inanimate agency. The philo- 
sophical cause is logically convertible with its effect ; but this 
is not true of those various causes in each of which the philo- 
sophical cause is wrapped up. In like manner, every logical 
antecedent contains within itself a necessitant condition of its 
consequent, and derives its life, or illative force, from that con- 
dition. Such exact and convertible necessitants occasionally 
present themselves in our reasonings, especially in the demon- 
stration of mathematical theorems. Ordinarily, however, care- 
ful discrimination is required to dissect them out of their 
envelopments. The discovery of them is the work only of 
philosophical thought. Yet even the simplest antecedent, if 
it be not itself a necessitant condition, can be shown to con- 
tain one. The consequence, "If there be motion, there is 
space," does not yield the converse, " If there be space, there 
is motion " ; nor is it easy to say at once what element or 
property of motion is a necessitant condition of space. But 



Chap. XIII. ] INFERENTIAL SEQUENCE. 113 

analysis answers this query. For motion involves increase or 
diminution of distance ; now where there is distance there is 
space, and where there is space there is distance. 

7. We can now state explicitly how the different modes of 
logical sequence are related to, and based upon, the law of Con- 
ditions. The existence of an entity is inferred as necessary 
when an antecedent either is or contains a necessitant con- 
dition. This is the law of positive apodeictic inference, or of 
the perception of the necessary to be. 

The inference of negative necessity — or of the necessary 
not to be — is yet more simply related to the law of Conditions. 
For a thing is necessarily non-existent so long as any of its 
conditions are non-existent. When, therefore, an antecedent 
either asserts or involves the non-existence of some condition 
of an entity, the non-existence of the entity is a necessary 
consequent. 

Along with the necessary non-existence of an entity, and 
from the same antecedent, we can infer the impossibility of 
its existence; and along with the necessary existence of a 
thing, and from the same antecedent, we can infer the impos- 
sibility of its non-existence. For negative necessity and posi- 
tive impossibility, as also positive necessity and negative 
impossibility, differ only as being different sides, or aspects, of 
the same consequence. 

But the impossibility ordinarily mentioned is the impossi- 
bility to be. For the human mind finds that it is easier and 
pleasanter to form a positive conception and then to reject it 
as incompatible with the antecedent, than it is immediately to 
conceive and to assert a thing to be necessarily non-existent. 
In like manner the necessity commonly mentioned is the 
necessity to be. 

Passing from apodeictic to problematic sequence we ask, 
" How are the inferences of the possible to be and of the pos- 
sible not to be, related to the law of Conditions ? " 

8. The possibility, like the necessity, of a thing is a rela- 
tion between the existence of it and that of other things. 
When a thing is necessary, its existence is absolutely coherent 
with that of other things : when it is possible, its existence is 



114 THE MODALIST. [Chap. XIII 

compatible with, that of other things. This compatibility may 
belong either to an actual or to a supposed object, and may, 
therefore, itself be either actual or supposed. The supposi- 
tional mode of possibility is that thought of when we infer a 
thing as possible ; for such inference is useful only when we 
do not know that the thing is, and yet can say that it may be. 

Possibility, whether belonging to an actual or to a supposed 
object, admits of degrees, the lowest of these being that exis- 
tential consistency which one thing may have with others, with 
which it has no special natural connection. Thus it is possi- 
ble that there should be a man, or a house, or a tree, upon a 
prairie. This degree of possibility is so far removed from 
proof, and even from suggestion, that it scarcely has a place 
in logic. Ordinarily, the possibility of an entity — its exis- 
tential compatibility with given circumstances — is more than 
mere consistency. It implies that the circumstances contain one 
or more of the proper, or special, conditions of the entity, and that, 
in this way, they present a suitability for its existence. When 
we say that, under such and such circumstances, a thing is, 
or would be, possible, we commonly mean, not simply that 
the circumstances would admit of the existence of the thing, 
but that they are specifically compatible with its existence, 
because they contain one or more of its necessary conditions. 

When an entity really or necessarily exists, all its conditions 
exist ; it is compatible with all its circumstances ; it is possi- 
ble in every respect, or in the highest degree. But this thor- 
ough-going compatibility, being recognized only when a thing 
is already perceived as real or as necessary, is seldom used as 
a ground of inference. And so it happens that the ordinary 
possibility of logical sequence is neither the weakest nor the 
strongest possibility, but is intermediate between the two. 
It is that conceived compatibility which arises upon our per- 
ceiving one or more of the conditions of an entity, while other 
conditions are not yet known either to exist or not to exist. 

This possibility may co-exist, or is consistent, with either 
necessity or impossibility. Tor, on the one hand, the discov- 
ery of conditions not yet known to exist may enable us to 
form a logical necessitant ; and, on the other hand, if investi- 



Chap. XIIL] INFERENTIAL SEQUENCE. 115 

gation shows some condition to be excluded from the given 
circumstances, the thing is impossible ; that is, it is necessary 
not to be. 

Hence it is evident that an entity is inferred as possible to be\ 
ivhen an antecedent, without justifying an apodeictic conclusion, 
either positive or negative, is, or contains, one or more of the 
conditions of the entity. In other words, the existence of a 
thing is inferred as possible when some of its conditions are 
known to exist, while the rest are not known either to exist 
or not to exist. 

9. The possible not to be is inferred from precisely the same \ 
antecedent as the possible to be, but the parts of the antece- 
dent are used differently. This might be expressed by saying 
that the non-existence of a thing is inferred as possible when 
some of its conditions are not known either to exist or not to exist, 
while some are known to exist. The reason for the first part of 
this statement is that when circumstances are not known to 
contain some conditions of an entity, the non-existence of the 
entity is compatible with the circumstances so far as they are 
known; the reason for the second part is that we have no 
inducement to enquire concerning the possibility of non-exist- 
ence except in cases which suggest the possibility of existence. 
The whole doctrine concerning both the inferences of possi- 
bility may be summed up in the statement that the possible, 
either to be or not to be, is inferred when some of the condi- 
tions of a thing are known to exist and some are not known 
either to exist or not to exist. But we must add that the 
inference of negative possibility is comparatively infrequent, 
and that, generally, the possible means the possible to be. 

10. We have seen that the possibility on which inference 
is based is a compatibility, and not a mere consistency. When 
this compatibility is so specific in its conditions as to be of a 
decided and noticeable character, it gives rise to a judgment of 
strong possibility, or of what has been called contingency. For 
we do not say that it is contingent to a man, or even to a man 
of talent, to write poetry, but to a poet : because, in this last 
case only, there is a special adaptedness for that work. This 
contingency may be said to approach necessity, for it always 



116 THE MODALIST. [Chap. XIII. 

suggests that an apodeictic antecedent may be found. Were 
the question whether a certain man made a well-fitting coat or 
not, and it were ascertained that he was in the tailoring busi- 
ness, the contingency thus arising would stimulate the search 
for a necessitating reason ; though in itself it would only jus- 
tify a judgment of strong possibility. 

This brings us to the last mode of logical sequence, namely, 
the inference of a thing as probable ; for this inference holds 
a place intermediate between those of contingency and of 
necessity. 

11. Every inference that an entity is possibly, or contin- 
gently, existent, may be accompanied by another, based on the 
same data, that it is possibly, perhaps contingently, non-exist- 
ent. Neither of these inferences, however, results in a definite 
confidence that the existence, or that the non-existence, is a 
fact ; we only say that each of these consequents is contingent 
or possible, and that, therefore, there is nothing absurd or un- 
natural in the supposition of it. Contingency, indeed, — the 
strengthened form of possibility — is accompanied with some 
expectancy ; but this is of an entirely weak and indeterminate 
character. 
. But, as it is certain that a thing must be either existent or 
' non-existent, it is plain that the confidence of certainty may, 
in any case, be definitely divided between the positive and the 
negative possibilities, provided only ice can determine what share 
belongs to each. Now this apportionment of confidence takes 
place whenever an antecedent of possibility, or of contingency, 
becomes so modified that it must be followed by some one of 
a number of events which are equally possible, and when the 
consequent enquired about is either one of these events, or 
is of such a nature as to agree with more than one. A draw- 
ing from a collection of variously colored balls in indefinite 
and unknown numbers, would be an antecedent of possibility 
with reference to the appearance of any individual ball first, 
or even of a red or of a white ball first. But, if we were in- 
formed that there were just thirty balls, twenty white and ten 
red, then — since the antecedent as modified by this knowledge 
gives the same amount of bounded, or limited, contingency, or 



Chap. XIII.] INFERENTIAL SEQUENCE. 117 

expectant possibility, for each ball — we say that the probability 
for the appearance of any individual ball is one-thirtieth, while 
that for a white ball is twenty-thirtieths, and that for a red 
ball, ten-thirtieths. 

The individual events, or consequents, conceived of and in- 
ferred as equally possible, and as the only possibilities in the 
case, and the number of which is the denominator of the frac- 
tion of probability, are called chances. 

Because the inference of probability has much in common 
with that of contingency, and may even be regarded as a 
modified inference of contingency, and because the same verbal 
forms are used to express both, they have often been classed 
together and called contingent inference. But they should not 
be confounded with one another. Both modes of inference 
will be discussed more fully hereafter. 



118 THE M0DALI8T. [Chap. XIV. 



CHAPTER XIV. 

ORTHOLOGIC INFERENCE. 

1. Inferences are also orthologic or homologic. 2. We infer, primarily 
and ordinarily, not from, but according to, the ultimate laws of inference. 

3. One individual fact may lie ortliologically inferred from another. 

4. The principles of orthologic inference are (a) logical, or universal; 
(6) semi-logical, or specific. 5. The logical laws are (a) those of identity, 
•contradiction, and excluded middle; which relate to the existence and 
non-existence of things; and (6) axiomatic principles concerning the 
common accidents of entity. 6. The semi-logical are (a) metaphysical 
axioms, (6) mathematical. 7. In orthologic inference (a) scrutinize the 
antecedent, (&) formulate the law. 8. The principle of identity is the 
unchangeableness of fact or truth. 9. It justifies (a) definitional substi- 
tution, (6) the synthesis of assertions, (c) the conversion of propositions, 
(d) analytic and subordinative judgments. 10. The law of contradiction 
supports (a) the rejection of absurdity, (6) the avoidance of inconsist- 
ency, (c) the reductio ad impossibile, (d) " contrapositive " inference. 
11. The law of excluded middle is logically prior to the other two ; and is 
used mostly in combination with the law of contradiction. This com- 
bination was Aristotle's "first of first principles." 

1. Some inferences attach their consequents to their antece- 
dents without referring to any previously known case of exis- 
tential connection. Others, referring to some previously per- 
eeived case of necessity or contingency, base their validity 
on the similarity of the antecedent now presented to that 
formerly perceived. Let us term those inferences whose valid- 
ity depends on this reference, homological; and those whose 
force is independent of any previous perception of connection, 
or consequence, ortJiological. Both these modes of illation 
take place in accordance with law; but they differ in that 
orthological inference follows a considerable variety of laws, 
while homological inference is based on. that one law which 
unites like consequents, whether of necessity or of contingency, 
with like antecedents. 



Chap. XIV.] OBTHOLOGIC INFERENCE. 119 

2. The laws of inference when definitely formnlated are 
termed " principles " of conviction ; and such of them as cannot 
be resolved into simpler laws are called " ultimate " principles. 
It was formerly taught that the mind has the power of imme- 
diately perceiving these ultimate principles, and that all infer- 
ence and reasoning depend on the application of them as rules 
to specific cases. Beyond question we sometimes reason in 
this way; and therefore, because of the order of our thought 
in such reasoning, the ultimate have also been styled the 
"first" principles of conviction. Nevertheless the doctrine, 
obscurely taught by Aristotle and more thoroughly advocated 
by Locke, that all our knowledge originates in the perception 
of particular facts and cases, and that general notions and 
principles are derived from individual perceptions by a process 
of analysis and abstraction, is indisputably true. First prin- 
ciples are "first" only as principles, or rules, not as perceptions ; 
and they are styled " self-evident " only because they are im- 
mediately and easily obtained from individual perceptions, and 
require no proof except that they be illustrated and tested by 
a reference to such perceptions. For while an axiom shows 
what elements in a case render a certain consequent necessary, 
it adds nothing to the certainty of the inference, and it may 
be unthought of, and even unknown, while yet one is reasoning 
in accordance with it. 

" I ask," says Locke, " is it not possible for a young lad to 
know that his whole body is bigger than his little finger, but 
by virtue of this maxim, that the whole is greater than a part, 
nor to be assured of it till he has learned that maxim ? Or 
cannot a country wench know that, having received a shilling 
from one that owes her three, and a shilling also from another 
that owes her three, the remaining debts in each of their 
hands are equal ? Cannot she know this, I say, without she 
fetch the certainty of it from this maxim, that, if you take 
equals from equals, the remainders will be equals, a maxim 
which possibly she never heard or thought of ? I desire any 
one to consider . . . which is known first and clearest by most 
people, the particular instance or the general rule ; and which 
it is that gives birth and life to the other." (Essay, Bk. iv. 12.) 



120 THE MOBALIST. [Chap. XIV. 

3. That we constantly reason without the use of first prin- 
ciples as rules should be especially borne in mind in connec- 
tion with orthologic inference. For this, primarily, is the 
inference of one individual fact from another with which it has 
some special necessary connection. The cases of inference men- 
tioned by Locke are orthologic, and evidently, though con- 
forming to general principles, they do not depend upon them ; 
nor do they depend upon any previously perceived case of 
similar sequence. 

Probably, as a matter of fact, the necessary relations of 
entity, together with the relata which they connect, are first 
perceived presentationally, and only afterwards are employed 
in inference. But our inferences concerning things as thus 
related, contain no reference to any such previous perceptions. 

Moreover, when conceiving of these relations, we recognize 
them, not merely as parts of an established or ordained con- 
stitution, but as absolutely necessary, and as belonging to that 
nature which things must have if they exist at all. Ortho- 
logical inference, therefore, as being specially related to the 
unchangeable constitution of things, is, in a pre-eminent sense, 
ontological. 

4. The classification of inferences is naturally the same 
with that of the principles on which they proceed, every prin- 
ciple being the formative law of the inferences corresponding 
to it ; moreover any mode of inference is best explained by 
stating clearly the principle according to which it takes place. 
Orthologic principles may be divided into two grand classes, 
which, for want of better terms, may be distinguished as the 
logical, or universal, and the semi-logical, or specific. The former 
pertain to all entites whatever ; the latter to different radical 
forms of entity, as such. We call the one class of principles 
logical, because the modes of conviction to which they give 
life are of unrestricted applicability, and are discussed in the 
general science of reasoning ; the other class of principles are 
semi-logical, because the logician, though distinctly recognizing 
their illative force, is not concerned about their specific nature 
and workings. 

5. The universal laws may be subdivided into two classes. 



Chap. XIV.] OBTHOLOGIC INFERENCE. 121 

The first of these concerns the existence and non-existence of 
things; and is composed of the three important laws of identity, 
contradiction and excluded middle. We shall endeavor, pres- 
ently, to explain these laws. The second class relates to all 
entities as having certain common "accidents" or properties, 
namely, individuality, quantity, and character, or nature. From 
these properties and the relations founded upon them, arise 
number, and numerical identity and difference ; also specific 
character, and identity and difference in kind; and also the 
conception of whole and parts ; whether of the metaphysical 
whole, or substance, and its attributes, or of the logical whole, 
or class of similars, and its members. 

The axiomatic principles pertaining to these universal as- 
pects of entity are such as the following: everything that 
exists must be an individual, and is numerically different from 
other things and numerically identical with itself, so that we 
can say " it is this, and not that " : — every entity has a nature 
of its own, in which, however, it more or less agrees with, or 
resembles, other entities ; so that it may be enrolled now in 
this logical class, now in that one: — every entity may be 
regarded as a metaphysical whole, or substantum, with attri- 
butal parts : — whatever is included in, or connected with, an 
attribute, is included in, or connected with, the whole thing, or 
substance ; but what is inconsistent with any attribute is in- 
consistent with the substance : — what is true of a class of 
entities distributively must be true of every subordinate class 
or individual : — when two things are each identical with a 
third, they are identical with each other; but when one is 
identical with a third and the other is different from it, they 
are different from each other: — in like manner, if each of 
two things agrees with a third in having some character or 
nature, they agree with each other ; but if one agrees and the 
other disagrees, they disagree with each other. To these 
axioms, or laws of necessity, postulates, or laws of possibility, 
might be added ; for example, what consists with an attribute 
may consist with the substance (or "substantial form"), and 
what is true of a specific class may be true of the generic. 

These and other universal principles, which relate to the 



122 THE M0DAL1ST. [Chap. XIV. 

common nature, rather than to the existence and non-existence, 
of entities, are interwoven with the very structure of human 
thought, and are the basis of important logical operations. 
Yet they are so simple, and so unobtrusive in their operation, 
that they are not often discussed at any length, but only 
referred to as self-evident. 

6. The second grand class of orthologic principles, the semi- 
logical, are those which support reasonings respecting specific 
modes of Being. They, also, may be subdivided into two 
classes ; the metaphysical and the mathematical. The former 
control our judgments respecting the most generic kinds of 
entity ; the latter, our specific reasonings regarding the quan- 
titative and spatial relations of things. 

Metaphysical axioms or laws, are such as these : Space and 
Time exist : — all other entities exist in space and in time : — 
Space and Time, though conditions of production and destruc- 
tion, cannot themselves be produced or destroyed: — every 
body occupies space : — two bodies cannot occupy the same 
space at the same time: — no body can be in two places at 
once : — no body can successively occupy two separate loca- 
tions without passing through the intermediate space: — all 
powers reside in substances, and are exercised by substances 
only : — every beginning or change is the result of the exercise 
of some power: — power acts only on or in substance : — power 
never acts without conditions, and the exercise of a power, 
together with its necessary conditions, constitutes a cause : — 
a cause and its effect (that is, the change consequent upon the 
cause) are inseparably united, so that neither can be present 
or absent without the presence or absence of the other: — 
every change corresponds in its nature to the cause producing 
it : — where there is no cause for a change, things remain as 
they are: — the cause of a cause is the cause of the effect: — 
a part of a part is part of the whole : — what resembles a like- 
ness resembles the original : — what excludes, or contains, a 
container, excludes, or contains, its contents. 

Mathematical axioms are such as these : Space admits geo- 
metrical figures and relations : — quantity admits of measure- 
ment and its relations : — a whole is equal to the sum of its 



Chap. XIV.] ORTHOLOGIC INFERENCE. 123 

parts : — a whole is greater than any of its parts : — a straight 
line is the shortest possible between two points : — through a 
given point one, and only one, straight line can be drawn 
parallel to a given straight line : — a straight line may meet 
another straight line so as to make two, and only two, equal 
adjacent angles ; and all the angles so made (that is, all right 
angles) are equal to one another : — angles, and other magni- 
tudes, which can be made to coincide with one another are 
equal : — solids of similar shape are equal if their boundaries 
are equal: — if a first thing be equal to a second which is equal 
to a third, the first is equal to the third : — if a first thing be 
greater than a second which is equal to, or greater than, a 
third, the first is greater than the third : — magnitudes of the 
same kind must be related to each other as equals, or as the 
greater and the less : — HA equal B, and C equal D, and if A 
be added to C, and B be added to D, the sum of A and C will 
equal the sum of B and D: — two straight lines parallel 
throughout any part of their course, will continue parallel 
however they may be prolonged. 

7. Such are the various classes of orthologic principles. To 
reason correctly in accordance with these principles requires 
care and thoughtfulness, but does not call for much artificial 
guidance. The act of inference, in itself, is very simple. 
Antecedent and consequent being considered in their relations, 
the latter is immediately asserted. The principal rule to be 
observed is that we should exercise careful scrutiny so as to 
determine what the antecedent presented may be, and whether 
it be adequate or not : and in this work it will help us if we 
state the inference in general terms and formulate the law on 
which its validity depends. Ordinarily this law can be ascer- 
tained without difficulty. 



8. Let us now recur to that triad of principles which relate 
to things simply as existing and as non-existent; for, while 
the importance of these laws is beyond dispute, the nature and 
use of them have not always been clearly apprehended. Let 
us note, first, that the principle of identity pertains to facts or 



124 THE MOBALIST. [Chap. XIV. 

statements which are identical with one another, and not to facts 
or statements of identity. That is, it no more pertains to these 
latter than to any other facts or statements. This principle 
asserts the unchangeableness of fact and truth. It has been 
expressed objectively by saying, " Whatever is, is ; and what- 
ever is not, is not," and subjectively by saying, "Whatever is 
true, is true ; and whatever is not true, is not true." These 
maxims are needless and useless as grounds of deductive in- 
ference; but they are fundamental laws of thought. They 
compel us either to abide by any statement already made or 
to confess that we have not spoken the truth ; and they re- 
quire us to accept a true statement a second time, or any 
number of times, even though it should be accompanied by 
non-essential additions, or modifications. 

9. The right to substitute the definition of a name or notion for 
the name or notion depends on the law of Identity. Common 
salt being chloride of sodium, it is an orthologic inference to 
say, "Good health involves the use of chloride of sodium, 
because good health involves the use of common salt." 

Again, the principle of Identity is employed when we combine 
two statements respecting the same subject; or unite equivalent modi- 
fications to both extremes of a proposition; ovjoin any two statements 
of a congruous nature, so as to make one compound assertion. 

Gold is a metal ; 

Gold is valuable ; therefore, 

Gold is a valuable metal. — 

is an inference made by combining two statements respecting 
the same subject. A precisely similar combination occurs in 
that transformation of thought which we call the substantial- 
ization of the predicate. Thus, 

Gold is a thing ; 

Gold is valuable ; therefore, 

Gold is a valuable thing, or a valuable. 

The following inferences result from adding equivalent 
modifications to both terms of a proposition : 

A negro is a fellow-creature ; therefore, 

A negro in suffering is a fellow- creature in suffering. 

Oxygen is an element ; therefore, 

To obtain oxygen is to obtain an element. 



Chap. XIV.] OBTHOLOGIC INFERENCE. 125 

The union of congruous statements yields sucli inferences 
as the following : 

Industry deserves reward ; and 

A negro is a fellow- creature ; therefore, 

An industrious negro is a fellow-creature deserving reward. 

Any synthetic statement may be justified when thus com- 
pounded of assertions which are individually correct. 

In the next place, that inference from substantal predications 
which logicians call conversion, is based on the law of Identity. 
Every substantal predication either asserts or denies the iden- 
tity of its subject with its predicate ; its converse makes the 
same assertion, though with a variation in the order and 
emphasis of thought. The predicate of any proposition having 
been, if necessary, substantialized and quantified — for example, 
" all men are mortal, being made " all men are some mortals " 
we immediately say, " some mortals are men — or all men." 

The conversion of substantal predications is that commonly 
mentioned, and is of special logical significance ; but any rela- 
tional assertion may be converted in a similar manner. The 
inferences, 

William is the husband of Anna ; therefore, 
Anna is the wife of William : 
A is equal to B ; therefore, 
B is equal to A — 

proceed on the principle of Identity. 

Finally, this principle may be used to justify the analytic, and 
the subordinative, judgments. In the former of these we predi- 
cate an attribute of a subject of which we already know the 
definition ; this predication may be considered a partial repeti- 
tion of the definition. In the latter we assert of some what 
we know to be true of all, and this may be considered a repeti- 
tion in part of the universal statement ; because, in thinking 
of the all, we may have thought of the some also. If, how- 
ever, it be objected that we do not always at first think of the 
some as being in the all, and of the attribute as being in the 
essence, this may be allowed. In that case the inference in 
question would follow, not the law of Identity, but principles 



126 THE MODALIST. [Chap. XIV. 

relating to the metaphysical and logical wholes. For any part 
of an essence must be an attribute of the substance; and 
what belongs to all must belong to some or any. This latter 
axiom is the dictum of Aristotle. 

10. The principle of Identity which compels us to maintain 
what we have learnt to be true, and to deny what we have 
ascertained to be false, operates in the mind more constantly 
than any other law of inference. But this operation almost 
evades our consciousness ; it is so easy and spontaneous. The 
law of Contradiction, on the contrary, is so frequently used for 
the rejection of error and the confirmation of truth that it was 
, held by Aristotle to be the first of all first principles. This law 
asserts that the presence of existence and the absence of non- 
existence — as also the absence of existence and the presence 
of non-existence — involve each other. Objectively, it says 
tha't the same thing cannot be and not be at the same time, but 
must either be or not be. Subjectively, it says that when a 
proposition (positive or negative) is true, the contradictory of 
it is false, and that when a proposition (positive or negative) 
is false, the contradictory of it is true. The first part of this 
law governs immediate contradictory denial, the second imme- 
diate contradictory affirmation. For the principle relates only 
to that contradiction which may take place when one proposi- 
tion sets forth the existence, and another the non-existence, of 
the very same thing. 

The chief use of the principle of Contradiction is indicated 
by its name. It enables us to assert that the opposite of what 
we have found to be true is false, and that the opposite of what 
we have found to be false is true. It so links together what is 
fact and what is not fact, what is true and what is not true in 
any respect regarding any subject, that, when either of these is 
known the other may be known also. Let " due " mean " not 
paid " ; then the debt, being paid, is not due ; being not 
paid, it is due ; being due, it is not paid ; or being not due, it 
is paid. So also we might contrast " present " and " absent." 

Because this law prevents us from believing in two opposite 
things at once Sir William Hamilton styles it the principle of 
non-contradiction; but the older name is to be preferred as 



Chap. XIV.] ORTHOLOGIC INFERENCE. 127 

giving the immediate effect of the law; which is the rejection 
of error as the opposite of truth, and the assertion of truth as 
the opposite of error. 

A specific use of the principle of Contradiction occurs in that 
method of argument known as the " reductio ad absurduni," or 
"ad impossible." If the immediate contradictory of an asser- 
tion be false, the assertion must be true. Let, us assume that 
contradictory as an antecedent and show that it leads to a false 
conclusion. This being done we say that the assumed contra- 
dictory must be false, and therefore, also, the original assertion 
true. For any antecedent which necessitates a false consequent 
must itself be false. That a straight line cannot meet the 
circumference of a circle in more than two points is proved as 
follows. "For if it could meet it in three or more points, all 
those points would be equally distant from the centre, and 
hence there would be three or more equal straight lines drawn 
from the same point to the same straight line. But this is 
impossible. Therefore the antecedent, contradictory of the 
original proposition, must be false ; and the original proposi- 
tion must be true." 

In the " reductio ad absurdum " the principle of Contradic- 
tion operates in connection with a course of reasoning which 
follows the general law of reason and consequent. In another 
mode of inference, which has been called "contraposition" 
the principle of Contradiction works alone. Let one of two 
predicates set forth the positive conception of a thing and the 
other the corresponding negative conception ; of course, then, 
the two propositions which apply these predicates to the same 
subject are immediately contradictory; for example, "the man 
is guilty," and "the man - is innocent." If, now, either of 
these propositions is affirmed the other may be denied, and if 
either be denied the other may be affirmed. Accordingly we 
say: 

The man is guilty ; therefore, 

The man is not innocent : — 

Every righteous man is happy ; therefore, 

No righteous man is unhappy : — 

Some possible cases are not probable ; therefore, 

Some possible cases are improbable. 



128 THE MODALIST. [Chap. XIV. 

In this mode of inference the conclusion sets a negative 
predicate over against the positive predicate of the premise,, 
or a positive over against the negative; and also opposes 
negation to affirmation, or affirmation to negation. Hence the 
name, " contra position." 

11. The last of those three principles mentioned for present 
discussion is the law of the Excluded Middle, or of the Ex- 
cluded Third. This law is inferior to the other two in fre- 
quency of use and in practical importance; yet is logically 
prior to them both, but especially to the law of contradiction. 
It declares that either the existence or the non-existence of a. 
thing is always a reality, and that there is no middle object 
of belief between positive and negative fact ; or rather no third 
object of belief at all. Erom this it follows that any proposi- 
tion and, of course, each of two immediate contradictories must 
be either true or false. Then the principle of Contradiction 
adds that one only is true, and that the other only is false. 

The law of Identity assumes a positive fact and asserts that 
it must remain so ; or a negative fact, and asserts that it must 
remain so. The law of Contradiction, assuming a positive fact, 
denies the negative assertion opposed to it ; or, assuming a 
negative fact, denies the positive assertion opposed to it. The 
law of Excluded Middle assumes neither positive nor negative 
fact, but only asserts that, in every case, there must be either 
one or other. Let some question be under investigation. 
Should, or should not, a protective tariff be levied? The 
Excluded Middle declares respecting each side of this question 
that it must be true or false : because there is no middle state 
possible either between being and non-being, or between truth 
and falsity; or rather no third alternative, of any descrip- 
tion, besides the existence and the non-existence of things, or- 
the truth and the falsity of propositions. Let us now find 
that one side (no matter which) is true. The law of Identity 
asserts that this opinion, if true, will remain true. Then the 
law of Contradiction adds that this side only is true, and that 
the other, alone, is false. And, once more, the law of Identity 
authorizes us to hold all that we have thus ascertained; at 
least till we discover ourselves to have been mistaken. 



Chap. XIV.] ORTHOLOGIC INFERENCE. 129 

The law of Excluded Middle is sometimes stated objectively 
by saying, "A thing must either be or not be," and subjectively, 
by saying, "Every assertion must be either true or false." 
These formulas, however, express the law only when they are 
taken in a weak sense. As the statement, " The man is either 
a knave or a fool " may signify merely that the man has one 
of these characters at least — not that he has one only ; so the 
statement, "A thing must either be or not be," might mean 
merely that every fact is either positive or negative — not that 
it may not be both at once. This last point, however, is in- 
cluded in the ordinary and stronger sense of the above formu- 
las. As the statement, " The man is either guilty or innocent " 
does not mean that he is either guilty or innocent, or both, but 
that, if he is not either of these two things, he is the other ; 
and that if he is either of them, he is not the other ; so the 
assertion, "A thing must either be or not be," naturally sig- 
nifies that one of these alternatives must be true — true only 
— if the other is false, and that one must be false — false 
only — if the other is true. This formula, therefore, unites 
the laws of Excluded Middle and of Contradiction in one 
compound law. 

This combination is sometimes called the law of Contradic- 
tion, sometimes the law of the Excluded Middle, and sometimes 
the principle of Contradiction and of the Excluded Middle. 
It is really the principle of Contradiction with that of the 
Excluded Middle prefixed to it That the law of Excluded 
Middle is of a subordinate character is evident from the fact 
that it is practically important only in this combination with 
the law of Contradiction, and as the basis for the operation of 
that law. 



130 THE MODALIST. [Chap. XV. 



CHAPTER XV. 

HOMOLOGIC INFERENCE. 

1. Proceeds on one principle. 2. Widens the operation of the law of 
Beason and Consequent. 3. Is based upon the law of Conditions. 4. Has 
three modes, (a) the paradigmatic, (6) the principiative, (c) the applicative. 
5. The common doctrine as to "deduction" and "induction." 6. The 
homologic principle (a) abbreviates ratiocination, (6) justifies the infer- 
ence of specific effects or causes, (c) enables us to "reason in the general." 

1. Okthologic inference accords with, and is supported by, 
many fundamental laws of existence and of thought. Homo- 
logic inference follows but one such, principle, namely, that 
similar antecedents are accompanied by similar consequents. 

This principle assumes that logical sequences depend, not 
on all the circumstances which a case may present, nor even 
on all those included in the antecedent, or reason, but only on 
certain essential conditions, which together constitute an exact 
antecedent. When we say that a cube of wood with a base 
two inches square must be eight times as large as a cube of 
gold on a base one inch square, this consequence is seen to 
depend on the geometrical nature and relations of the things 
mentioned; and is only accidentally connected with the color, 
the weight, the chemical constitution, the physical properties, 
and the commercial value, of the cubes compared. Hence, in 
ordinary inference, though the antecedent is conceived of as 
including more than the necessitating conditions of the con- 
sequent, it is never conceived of as including all the circum- 
stances perceivable in the case; many of these are neglected 
as non-essential. Our thought may even be so specially 
directed to the points on which the sequence depends, that it 
may be confined to a consideration of these points alone. 
Therefore inference, even when it may take place without 



Chap. XV.] HOMOLOGIC INFEBENCE. 131 

generalization, commonly involves more or less precision and 
abstraction in the perception of the antecedent. 

2. The homologic principle asserts that, whenever given cir- 
cumstances contain an antecedent similar to one already found to 
have a certain consequent, we may infer a similar consequent in 
connection with the similar antecedent. This law resembles that 
according to which like causes are inferred from like effects 
and like effects from like causes ; but it is much more compre- 
hensive, because it relates to every ground of logical connec- 
tion. A conclusion based on it is said to follow by " parity of 
reasoning " ; and claims the same degree of confidence with 
the prior conclusion, provided the antecedent on which it 
depends, is precisely similar to the antecedent of the prior 
conclusion. This exact similarity is what is meant by "logi- 
cal identity," and is often expressed by saying that the reason 
for the second conclusion is "the same " as that for the first. 

3. The homologic principle, like that of inference in gen- 
eral, is closely related to the law of Conditions. It is based 
on the ontological law that like entities are controlled by 
like conditions ; and this is an essential, though a subordi- 
nate, part of the general law of Conditions. Hence, too, in 
accordance with its origin, the homologic principle is a kind 
of attachment, which works in connection with the principle 
of Eeason and Consequent ; and which applies equally to every 
mode and degree of inference. Whether a sequence be apo- 
deictic or problematic, actualistic or hypothetical, a similar con- 
sequent may always be inferred from a similar antecedent. 

4. While homologic inference, unlike orthologic, obeys only 
one law, it assumes three different forms, or modes, according 
to the development of thought and perception in conjunction 
with which it is experienced. For either we may immediately 
infer one individual sequence from another ; or we may infer 
general principles from individual sequences ; or we may infer 
individual or particular sequences from general principles. 

These three modes of inference may be distinguished as the 
paradigmatic, the principiative 3 and the applicative. 

The first is named paradigmatic inference, or paradigmatiza- 
tion, because it is immediately founded on the use of an exam- 






132 THE MOBALIST. [Chap. XV. 

pie (TrapdSayfia), or individual instance parallel to the case in 
question. Aristotle mentions this mode of inference, but 
teaches that we first infer a general principle from the in- 
stance, or instances, given, and then, in turn, infer the indi- 
vidual or particular conclusion from that. Such a process, 
however, is not necessary, and does not always take place. 
The perception that one fact is logically followed by another 
involves, as we have said, some abstraction and precision in 
determining the antecedent, and more or less rejection of non- 
essential circumstances ; and this abstraction often results in 
the formation of a rule of judgment : but we can reason to a 
parallel case without any such rule. If only we perceive that 
given circumstances contain a new antecedent similar to that 
already observed, we may immediately infer a similar conse- 
quent. The child who has enjoyed the sweetness of one lump 
of sugar, cries for another lump, not because of the general 
truth that sugar is sweet, but because he expects the second 
lump to affect him in the same way as the first. And the 
mathematician, who has demonstrated, orthologically, that the 
sum of the angles of the plane triangle A is equal to two right 
angles, immediately infers, homologically, that the sum of the 
angles of B, another plane triangle, are also equal to two 
right angles. 

The second mode of homologic inference is equally depend- 
ent with the first on the law that like consequents follow like 
antecedents ; yet perhaps not so evidently. In principiation 
the terms of a sequence, after being conceived precisely, or 
abstractly, are divested of their individuality ; and thus yield a 
general rule, or principle. This rule is valid only because any 
antecedent to which it may apply, must be like the first found 
antecedent, and must, therefore, have a consequent similar to 
the first consequent. 

Principiation is the generalization of a sequence. It is more 
than the generalization of thought ; inasmuch as the forms of 
thought produced by it are accompanied with conviction. 
Neither can this process be adequately designated by the term 
" induction." Induction is only that species of principiation 
by which the laws, or general causational sequences, of Nature, 



Chap. XV.] HOMOLOGIC INFERENCE, 133 

are determined. Any general truth whatever — for example,, 
any axiom or postulate of mathematics or of metaphysics — 
may be obtained by principiation. This, indeed, is the only 
way in which axiomatic truth is originally obtained. The doc- 
trine that all general principles, or rules of reasoning, are 
derived by principiation from perceptions of individual con- 
nections, or sequences, is the first and most fundamental prin- 
ciple of philosophical method. 

Principiated truth is chiefly valuable because it may be 
stored up in the mind as a basis for future inference. For 
whenever afterwards a case arises such as a general principle 
contemplates, we can infer a consequent such as that principle 
requires. And this inference we style " applicative," because 
it consists in the application of the general truth to the par- 
ticular case. It evidently depends wholly on the homologic 
law. 

5. Most logicians distinguish this applicative inference as. 
deduction, because it is the "bringing down" of a general 
principle to a specific case. This use of language need not be 
rejected; though the word "deduction" may signify "bringing 
from" as well as "bringing down," and often indicates any 
kind of formal inference. But a serious error is inculcated 
when deduction, — that is, applicative inference — is contrasted 
with induction, and we are taught that all inference belongs 
to one or other of these two modes. Deduction, or applica- 
tion, should be contrasted with principiation, of which induc- 
tion is only an important species ; and then even principiation 
and deduction, so far from being the only modes of inference, 
are merely the more formal modes of homologic inference. 

6. Kegarding, now, this kind of inference in the general,, 
let us note that our use of it results in three practical benefits. 
For, in the first place, the homologic law abbreviates reason- 
ing. A mathematician, having discovered, by a course of 
demonstration, that the solidity of a cone is measured by one 
third the product of its base and altitude, immediately em- 
ploys this method of calculation for another cone, and for all 
cones. The solution of the individual problem is accepted as 
the solution of others exactly similar. It originates a general 



134 THE MODALIST. [Chap. XV. 

truth, a law of inference. Without the homologic principle 
we might conceive of such a law, but we would have no ground 
to believe that it expressed truth. 

In the next place, the homologic principle enables us to 
foretell natural consequences, and to ascribe effects to their 
proper causes. In such judgments, we do not simply substi- 
tute a shorter process for a longer one ; we form specific infer- 
ences which could not be formed in any other way. Those 
judgments and reasonings which are based purely on the nec- 
essary nature of things may take place orthologically, and 
without reference to any previously perceived case of similar 
connection : the homologic principle may be dispensed with in 
such reasonings ; it only renders them shorter and easier, as 
in the case of mathematical calculations and demonstrations. 
But inferential judgments concerning specific causational 
relations must rest on previously perceived cases of similar 
connection, or consequence ; they must be formed homologi- 
cally. For the peculiarities of specific causes and effects are 
perceived only as belonging to the actual constitution of the 
Universe— not as belonging to the necessary nature of things. 
These peculiarities appear to have been ordained by the power 
which first created and constituted the Universe and its com- 
ponent parts. They become known to us only by actual 
observation, or experience. We can, without reference to pre- 
vious experience, say that every change or beginning of exist- 
ence must have some cause, and that similar powers under 
similar conditions will produce similar results ; but we cannot 
tell, except from a previously observed case, that a specific 
causational antecedent, and a specific causational consequent, 
will accompany each other. 

Inductive principiation, therefore, differs from axiomatic, 
and inductive reasoning in general from that which is mathe- 
matical or metaphysical (or ontological), in that the former is 
necessarily founded on observation ; which is not the case with 
the latter. 

Thirdly, and finally, the homologic principle justifies rea- 
soning in the general, so that a process of argument may be 
conducted throughout, and its conclusion given, in general 



Chap. XV.] HOMOLOGIC INFERENCE. 135 

terms; after which, of course, the conclusion may be applied 
to any individual case, or cases. We have seen how every 
individual inference may, through principiation, yield a general 
inference, or law of reasoning. Should there now be a series 
of such principles, or generalized inferences, so related to each 
other that the antecedent of the second is the consequent of 
the first, the antecedent of the third the consequent of the 
second, the antecedent of the fourth the consequent of the 
third, and so on to the end of the series, it is clear that the last 
consequent may be inferred from the first antecedent. Because 
the antecedent of an antecedent is the antecedent of the con- 
sequent also. And evidently that same homologic principle 
which justifies the formation of general inferential propositions, 
also renders it possible for us thus to reason consecutively by 
means of them. 

The great merit of the Aristotelian doctrine of the syllogism 
is that it sets forth the laws and forms of the correct sequence 
of generalized inferences ; and so supplies a test of all reason- 
ing. For every step in a course of reasoning, except the 
application of the conclusion to some individual case, or cases, 
may be conceived and expressed in the general. 



136 THE MODALIST. [Chap. XVI. 



CHAPTER XVI. 

INDUCTIVE KEASONING. 

1. Induction, the principiation of causational sequence. 2. Often signi- 
fies, not this act, but a process ; 3. In which there are five stages : (a) ob- 
servation, (6) supposition, (c) principiation, (d) criticism and suggestion, 
(e) deduction. 4. Observation includes experiment. 5. Inductional sup- 
position is an homologic suggestion, and involves more than the association 
of ideas. 6. Inductive principiation is the essential part of the process, 
7. Scientific criticism argues from (a) the ontological law of causation, 
(b) the ascertained constitution of the universe. 8. Inductional deduc- 
tion. 9. The maxims of scientific suggestion imply that Nature has ' ' an 
intellectual constitution." 10. They assert that Nature (a) has a fixedness 
of operation, (&) abounds in analogies, (c) uses reliable signs, (d) is par- 
simonious of instrumentalities, (e) is simple in her methods, and (/) is 
governed by design, or Final Cause. 11. Ontological principles determine 
(a) the method of agreement, (6) the method of difference, (c) the in- 
direct, or analogical, method of difference, (d) the method of residues, 
and (e) the method of concomitant variations, 

1. The word "induction" primarily signifies that act of 
principiation in which, some law of causational sequence is 
inferred from the perception of some individual sequence, or 
sequences. This act presupposes causational antecedents and 
consequents. A causational antecedent is any definite com- 
bination of circumstances which has and exercises the power 
to produce a given consequent. It therefore always includes, 
or implies, an efficient agent and the conditions of its opera- 
tion, or the conjunction of such agents and their operations ; 
but it may also include other elements in union with these. 
The efficient agent, or set of agents, and the conditions of its 
operation, are the exact philosophical cause of an effect, and in 
a manner reciprocate with the effect ; for they may always be 
inferred from the effect. Thus the rising of the sun is the exact, 
or reciprocating, cause of day; and a certain combination of 



Chap. XVI. ] INDUCTIVE REASONING. 137 

sodium and chlorine is the exact cause of salt. In such cases 
we may infer effect from cause, and cause from effect. But an 
ordinary cause contains the exact cause within some envelop- 
ment or other ; so that the same effect is often said to result 
now from this cause and now from that one. The burning of 
fuel is a cause of heat, but it is only one out of a number of 
causes ; and extreme disease is only one particular, or specific, 
cause of death. To determine in any case what should be 
regarded as the cause, or causal antecedent, of a given effect 
is not always easy when we are only seeking to define some 
specific cause; and it is often very difficult when we would 
clearly discern a reciprocating cause. But, in either case, 
after that determination, the act of induction which follows is 
perfectly simple. It is merely a generalization based on the 
homologic principle. 

2. Frequently, however, because of the importance of the 
principiative act, the word " induction " is used comprehen- 
sively, and signifies a process in which principiation is only an 
essential part ; so that commonly, when we say that a principle 
has been ascertained by induction, or by inductive reasoning, 
we mean that some law has been determined by a process 
which has terminated in principiation. Sometimes, even, we 
speak of an individual or particular conclusion being reached 
inductively, because we have come to it through a process in 
which we first gain a general principle and then apply that 
principle. 

3. This process of inductive reasoning varies in the extent 
and variety of its parts, according to the requirements of each 
case; but in its fullest development may be divided into five 
parts, or stages. First, there is a careful observation and a 
" simple enumeration" of those facts, or phenomena, which 
appear to contain " instances " of the sequence to be investi- 
gated ; secondly, there is a more or less definite apprehension 
or conception of the sequence in the individual cases, following 
upon an analysis of each instance, things evidently non- 
essential being rejected; thirdly, there is the act of induction, 
or principiation ; fourthly, a critical testing and elaboration of 
the law, whereby our conception of it is rendered more ade- 



138 THE MODALIST. [Chap. XVI. 

quate and truthful ; and whereby also we may be prepared for 
the apprehension of some higher law ; and fifthly ', there may 
be a deduction from the law in combining it with other laws 
already ascertained, or in applying it to individual cases. 

4. The first of these stages, while presenting no theoretical 
difficulty, demands diligence and skill from the investigator. 
At least, great pains are necessary if we would ascertain the 
less patent laws of the Universe. Long journeys, costly instru- 
ments, accurate records, the watching and waiting of years, 
may be called for. Moreover, Nature must often be made to 
work under conditions furnished by the student, in order that 
the results of experiment may be added to those of simple 
observation. 

5. The second step in inductive reasoning — that is, our first 
formal conception of the sequence — involves some power of 
penetrative and constructive judgment. It would be impossible 
if the human mind could not often perceive causational se- 
quences, as such ; or if, in cases of question, we could not form 
a more or less probable supposition, or hypothesis, regarding 
the character of a cause, or of an effect. Inasmuch as we do not 
directly observe any force, or efficiency, producing the changes 
which occur around us, but only a succession of phenomena, 
or events, some philosophers have denied that the relation of 
cause and effect is anything more than uniformity of suc- 
cession; they have taught that our apparent perception of 
power, or force, is either a delusion of the mind, or, at the 
most, a form of thought which the mind imposes on phenomena, 
and which has no objective significance, although, perhaps, it 
may represent a unity — or a strong association — of ideas. 
Such teachings are unsatisfactory ; instead of explaining, they 
explain away what every human being naturally and neces- 
sarily believes. We prefer that doctrine which asserts that 
all man's knowledge of the causal relation, and of specific causes 
and effects, originates in his perception of those changes which 
take place ivithin, or in immediate connection with, his own body 
and his own soul. 

The various powers and operations of spirit are seen through 
self-consciousness ; while the essential attributes of matter 



Chap. XVI.] INDUCTIVE REASONING. 139 

and the specific qualities of material substances, become known 
to us as related to our own bodily efforts and sensations. 
Solidity, or the space-filling quality, is first perceived as be- 
longing to the members of our own bodies, and is then inf eren- 
tially assigned to things about us. This is the case also with 
that force, or power of propulsion, which shows itself in mus- 
cular exertion and resistance. The sense-affecting qualities of 
objects are powers residing in them ; and which we ascribe to 
them because we find them to exert these powers upon us on 
the recurrence of the proper conditions. 

The full discussion of the law of cause and effect, and of 
specific causational perceptions, belongs to metaphysical psy- 
chology. What has now been said may indicate in what way 
the mind becomes qualified to distinguish between a true 
causational sequence and an accidental succession of events. 
The power to recognize causes is a logical outgrowth of man's 
original and immediate perceptions; nor is there any rule 
whereby causal may be surely distinguished from merely tem- 
poral antecedents except that a cause always involves effi- 
ciency, and that our recognition of any kind of efficiency must 
be founded on a first knowledge gained in man's personal 
experience. 

Those suppositions, or hypotheses, which we form when 
only some conditions of a causational sequence can be seen 
and others must be conjectured, yet more evidently than our 
unquestioned perceptions, are based on the knowledge which 
we already possess of causes and causal laws. They are not 
free imaginings ; they are conceptions of antecedents in which 
causes and conditions more or less similar to others already 
known, are so combined that they may be supposed capable of 
accomplishing given results. This is the origin both of theo- 
ries by which phenomena are explained, and of practical inven- 
tions by which phenomena are produced. Therefore, also, no 
man is properly qualified to make discoveries or inventions 
who has not mastered all the knowledge which bears in any 
way on the field of his investigations. 

6. When a causational sequence is obviously and exactly 
perceived by the observant student, as, for example, often hap- 



140 THE MODALIST. [Chap. XVI. 

pens in decisive chemical experiments, the process of inquiry 
may be made to close with that generalization, or principia- 
tion, which has been mentioned as the third step in inductive 
reasoning. 

7. But if the student has only formed a probable or incom- 
plete hypothesis, a fourth stage of investigation is necessary 
in order to remove the doubt, or to remedy the imperfection : 
the judgment, or hypothesis, which has been formed must be 
subjected to a process of trial and amendment. This process 
is not of the nature of principiation ; neither is it essentially 
deductive, though it may be regulated by rules. It consists of 
a further questioning of instances and experiments, both new 
and old, together with a more methodical interpretation of 
them according to those relations by which causes are per- 
ceived to be conditioned. For, in our cognition of causes 
and effects, we intuitively perceive such things as the follow- 
ing to be necessary, viz., that, in the absence of any cause 
there is no change, so that things remain as they are — that 
every change has an adequate cause, or a variety of adequate 
causes, so that, if the effect take place, some adequate cause 
may be inferred ; but if the effect do not take place, no ade- 
quate cause exists for it — that a part of a cause may exist 
without any production of the effect ; but that, if an effect take 
place, every part of the cause producing it must have existed 
— that a conjunction of effects and a corresponding conjunc- 
tion of causes involve each other — and that the same cause 
(that is, the same, or a precisely similar, potency, or combina- 
tion of potencies, under the same combination of conditions) 
produces the same effect. These judgments are intuitive per- 
ceptions of the direct, and of the corollary, workings of the great 
ontological law of causation. We make them constantly in 
cases which frequently occur, and finally, by principiation, 
derive from them those rules which are the fundamental 
canons of inductive — or inductional — criticism. 

8. After a law of causation has been determined, either 
directly or after critical elaboration, it may be applied to the 
inference of individual consequents. The result so obtained, 
because it is the ending of an inductive process, is sometimes 



Chap. XVI.] INDUCTIVE REASONING. 141 

said to be reached inductively. And, with more reason, per- 
haps, the same language is employed when two or more laws 
of causation are combined so as to form a new compound law. 
For, though this also is a case of deduction, it is doubly the 
result of inductive reasoning. Important inquiries have been 
answered in this way; and this is likely to occur more fre- 
quently as the knowledge of principles increases. Hence 
many think that deduction will hereafter share, equally with 
principiation, in the honors of scientific progress. 



9. We have now briefly sketched those mental operations 
whereby we arrive at conclusions regarding causational se- 
quences, and which are often grouped under the head of 
" Inductive Reasoning." If our analysis of these operations 
be correct, it will prepare us to understand philosophically a 
certain set of maxims which have always guided scientific con- 
jecture, and a certain set of rules whereby scientific theories 
are often tested. 

The maxims to which we refer are all connected with a 
belief, universally diffused among men, that Nature, or the 
Universe, has an orderly, and, if we may so speak, an intel- 
lectual, constitution. We do not mean by this that Nature 
possesses any power of thinking, but only that the Universe, 
in all its departments, is evidently the production of rational 
plan and purpose; and therefore, also, is such as rational 
thought can understand and appreciate. Some explain this 
conviction as. an immediate intuition of the mind; it seems 
nothing more than an homological inference from the forma- 
tion and use of plans and instrumentalities by man himself. 
Observation shows that intelligence is the only knowable cause 
for any continued and complicated adjustment of means to 
desirable ends ; and reflection on the nature of things convinces 
us that no other conceivable cause can adequately account for 
such an adjustment. Therefore, discovering wise adaptations, 
first in one natural arrangement and then in another, we spon- 
taneously conclude that rational methods pervade every part 
of the Universe. Moreover, men become greatly confirmed in 



142 THE MODALIST. [Chap. XVI. 

this conclusion as they progress in their knowledge of the 
works of Nature. 

Such is the origin of those directive maxims which presup- 
pose the intellectuality of the Universe. They are not self- 
evident truths, but the results of observation and thought;, 
and they may be regarded as fundamental parts of that prior 
knowledge which qualifies one for the second stage of the 
inductive process — that is, for the true apprehension of a 
sequence, or for wise conjecture concerning it. 

10. The most common of these maxims asserts that the 
course of Nature is fixed and uniform. By this we are not to 
understand that the arrangements of the Universe are abso- 
lutely unchangeable, but only that they have a permanence 
which characterizes every wisely formed constitution of things ; 
nor are we to understand that Nature is wanting in variety j. 
for her variety is multitudinous ; but only that lines of law 
and order are traceable in every department of the Creation.. 
The Universe, animate, or inanimate, organic or inorganic, is; 
composed of genera and species of things. Each of these con- 
forms to a certain type and has its own method of existence ; 
and can, therefore, be rationally comprehended. Hence the 
different branches of scientific knowledge correspond to differ- 
ent systems of permanent uniformities. 

The maxim that Nature abounds in analogies is little else- 
than a corollary of that just considered. When we prefer one- 
theory to another because it accords better with the analogy 
of Nature, we simply recognize the intellectual unity and. 
stability of the Universe. For, as a matter of fact, Nature is. 
found to use similar methods to effect similar ends, even 
though quite other methods might have been employed. A 
notable instance of this is the radical similarity in bodily 
structure of all the larger animals, whether beasts, birds, or 
fishes, even while the greatest dissimilarities arise in accor- 
dance with the necessities of their different spheres of life. 

In the next place, it is constantly assumed by scientific men 
that Nature uses reliable signs to indicate her agencies. There- 
might be a universe in which like causes, or agencies, would 
always produce like effects, but in which, nevertheless, we 



Chap. XVI.] INDUCTIVE BEASONIJVG. 143 

could not be confident that any agency which seemed to us of 
a given kind was really so. But now, in the constitutions of 
things, immediately perceptible qualities have been so united 
to other qualities that they may be takeo as indications of the 
entire natures to which they belong. Every kind of metal has 
a color and a specific gravity which mark that metal only ; and 
which suggest and represent to us the whole complex of its 
qualities. The appearance of any animal, or insect, or plant, 
of any fruit or seed, brings before us the complete natural his- 
tory of one specific organism. In short, Nature takes pains, 
not only that her methods should be fixed and orderly, but 
also that they should be easily apprehended by beings of a 
finite intelligence. Besting on fixed and observable signs, and 
•exercising proper diligence, man obtains a usable knowledge 
of causes and becomes qualified for the control and manage- 
ment of natural agencies. 

Again, superintending wisdom is recognized in the maxim 
that Nature, though lavish of her expedients, is parsimonious 
of her instrumentalities. She accomplishes an immense variety 
of results with the smallest possible variety of agents. How- 
ever peculiar a proolem may be, no new agency is introduced 
nnless it be necessary ; there is rather some extraordinary 
modification of an ordinary agency; as may be seen in the 
trunk of the elephant, the tail of the otter, and the wings of 
the flying fish. A perception of this parsimony in the use of 
powers and instruments gave rise to the adage "Entia non 
sunt multiplicanda praeter necessitatem." If phenomena can 
be explained as well by supposing one kind of agent as by 
supposing two, or as well by supposing two as by supposing 
three, the preference is to be given to the smaller number. 
Because differences of specific gravity account for the heavi- 
ness of some bodies and the lightness of others, only one 
agency is recognized in both these phenomena. The law of 
gravitation is found sufficiently to account for the continued 
motion of the heavenly bodies; and therefore we reject the 
supposition of any peculiar celestial force. In like manner, 
the hypothesis that, in the successive stages of creation, cer- 
tain organic forms were built upon others and immediately 



144 THE MODALIST. [Chap. XVI. 

produced by giving to a departing species the power to pro- 
duce a successor better qualified for life under new conditions, 
cannot be condemned as unphilosophical, unless it should be 
found to conflict with fact. It may relate, however, not to the 
workings of Nature, but of the power that produced Nature. 

Closely allied to the law of parsimony, and perhaps radically 
identical with it, is the maxim that Nature is simple in her 
methods. Scientific men always prefer the simpler explanation, 
provided that, in other respects, it is equally satisfactory with 
the more complex. But this simplicity of Nature is to be 
understood in a relative rather than in an absolute sense. 
Some of her arrangements are complicated, and resemble very 
ingeniously constructed instruments or machines. This is 
always the case when the work to be done includes a large 
variety of movements or functions, such as are provided for in 
the mechanism of the human arm, or eye, or of man's body as 
a whole. Yet, however complicated a natural organism may 
be, the thoughtful student is amazed both at the simplicity 
of its several contrivances, and at the neatness with which 
they are united in one effective arrangement. No part of the 
system is superfluous, or out of place. 

Finally, the intellectuality of the Universe is expressly as- 
serted in the doctrine, that Mature is governed by final causes, or 
by intelligent design — that wisdom operates in the Universe 
through means adapted to the accomplishment of ends. This 
doctrine has always influenced speculation; and has always 
been a teaching of philosophy. Nor need we wonder at this, 
since the doctrine only expresses a natural and rational judg- 
ment. The Stoic aphorism, "God and Nature do nothing in 
vain" (6 #eos /cat rj <f>v(n<; ovSev fxanqv ttoiovvlv) , and Aristotle's 
conception of the final cause (to ov-cvcko.), simply formulate a 
general conviction of mankind in regard to the origin of the 
phenomena of the Universe. For the Peripatetic division of 
causes, or rather of causal conditions, into the material, the 
formal, the efficient, and the final, is not really a theory of 
causation in the abstract, but a cosmogony. It analyzes the 
causal antecedent of the Universe into four constituents — one 
of these being design. 



Chap. XVI.] INDUCTIVE REASONING. 145 

Moreover, it is worthy of remark that Aristotle did not con- 
sider the world to be itself capable of thinking or deliberation ; 
for, he says, that would be " as if the art of ship-building were 
in the timber," or as if any machine had the intelligence to 
construct itself. Indeed, the fact that Nature, notwithstand- 
ing her wonderful excellence, sometimes produces abortions 
and monstrosities, indicates an imperfection which probably 
is inherent in every created agency. In herself Nature is only 
a marvellous system of powers and laws which operates 
throughout the Universe, and which, though unintelligent, 
may be termed intellectual, because it is the production and 
the reflection of creative thought. 

By some philosophers inquiry after final causes has been 
condemned as fruitless. This objection applies only to cases 
in which conjectures are made without adequate support in 
existing analogies, and are rested upon as probable without 
experimental evidence. Mere theorizing respecting the work 
for which some arrangement or agency is designed, when 
separated from the observation and investigation of facts, has 
originated many strange explanations of natural phenomena ; 
and is worse than fruitless. But hypotheses formed after the 
analogy of known adaptations, and followed by investigation, 
have often led to the discovery of truth. Harvey, observing 
valves in the veins and in the heart, first conjectured, and 
then discovered, the circulation of the blood. Physiologists 
discuss every bodily part in the light of some end for which 
they suppose it to be intended ; and they declare that every 
part is an organ, with a function of its own. 

11. Let us now glance at those canons of experimental 
enquiry, whereby hypotheses are tested, and which are used 
chiefly in the fourth, or critical, stage of inductive reasoning. 
For rules are not needed when every causal condition of a 
sequence is clearly perceptible, but only when the exact nature 
of the cause is in doubt. This is especially the case when the 
cause of some effect is involved in a confusing complex of 
circumstances ; then a work of determination and of elimi- 
nation becomes necessary. A less or a greater number of 
directions may be given for this work according to the com- 



146 THE MODALIST. [Chap. XVI. 

prehensiveness of each rule, but the following five canons dis- 
cussed by Mr. J. S. Mill, under the head of "methods of 
induction," are certainly such as every careful thinker must 
use. They are all outgrowths of the radical law of causational 
sequence. 

The first rule is that which governs the " method of agree- 
ment." When two or more cases of sequence, which have the 
same consequent, have only one circumstance, or set of cir- 
cumstances, in common, the antecedent of the consequent is 
to be sought for in their common part. If a certain fever 
prevail in two or more localities, in both of which the air is 
tainted from decaying vegetation, but which differ in all other 
respects, we say that malaria is the cause, or an essential part 
of the cause, of the fever. If cucumbers thrive whenever they 
are planted in rich mellow earth, and enjoy an abundance of 
warmth, light, and moisture, and if they call for these con- 
ditions only, we say that we have found the right way for the 
cultivation of cucumbers. 

The second rule controls the ''method of difference" If 
various cases which produce a sequence differ, severally, from 
other cases which do not produce it, only in the presence of 
a certain antecedent which is uniformly absent when the 
sequence is absent, that antecedent is, wholly, or partly, the 
cause of the sequence. If, on the other hand, a supposed 
cause be found present in cases where the sequence does not 
occur, as well as in cases in which it does occur, it cannot be 
a true and sufficient cause. Since dew falls always on clear 
nights, but never when the sky is clouded, we ascribe the 
formation of dew to the cooling of the surface of the earth by 
radiation. Since all living things breathe the air, and cease 
to live when prevented from breathing it, we say that air is 
essential to animal life. The method of difference presup- 
poses the method of agreement, and is built on it. It is appli- 
cable whenever a given consequent fails to occur, and this 
failure is either in accordance with our expectation or in 
opposition to it. If the failure take place in accordance with 
our expectation and along with the absence of the supposed 
antecedent, our theory is confirmed ; but if it fail in opposition 



Chap. XVI.] INDUCTIVE REASONING. 147 

to our expectation and notwithstanding the occurrence of the 
supposed antecedent, our theory must be rejected. If a cer- 
tain compound, expected to explode on ignition, will not 
explode, our conception of the antecedent is evidently wrong. 
After learning this, if we still desire to find a new explosive 
mixture, we must amend our hypothesis, and renew our experi- 
ments and our examination of instances. 

Sometimes a single instance of a sequence, being distinct and 
free from all complication, is sufficient to determine a law. 
Yet oftener a pair of experiments, or observations, one using 
an antecedent and the other leaving it out, are sufficient. In 
such cases we can scarcely be said to need or to follow either 
the method of agreement or that of difference; we simply 
decide at once according to the principles of the law of causa- 
tion. But when elimination and determination are necessary, 
we are greatly helped by analyzing a number of instances. 

The third rule sets forth the indirect method of difference. 
Sometimes no cases of the non-occurrence of a consequent can 
be found which differ from cases of its occurrence merely in 
the absence of some antecedent. If then we only can find 
cases of the non-occurrence, which are more or less similar to 
the cases of the occurrence except as to the presence of any 
similar antecedent, we may consider that antecedent to be 
wholly, or partly, the true cause. No species of quadruped, or 
other animal that is warm-blooded, differs from the ordinary 
quadruped, or other animal, in being cold-blooded. But we can 
find animals that are cold-blooded, and we may reason from 
their constitution by a kind of negative analogy. Thus, says 
Mr. Mill, "If it be true that all animals which have a well- 
developed respiratory system, and therefore aerate the blood 
perfectly, agree in being warm-blooded, wliile those whose res- 
piratory system is imperfect do not maintain a temperature 
much exceeding that of the surrounding medium, we may 
argue from this two-fold experience, that the change which 
takes place in the blood by respiration, is the cause of animal 
heat." This third method is simply a special form of the 
method of difference; and is guided by a reference to the 
analogies of Nature. 



148 THE MODALIST. [Chap. XVI. 

The fourth rule presents what Mr. Mill calls the " method of 
residues" If we subduct from any complex of phenomena 
such parts as are known to be the effects of certain antece- 
dents, the cause of the residual phenomenon, or phenomena, is 
to be found in the residue of the antecedents. This method 
endeavors to isolate a case mentally which cannot be isolated 
in fact. The principle of it is that by which we find the 
weight of a load of hay in subtracting the weight of the wagon 
from that of the wagon and the load. But by the observation 
of residues we determine separate kinds of causes or of opera- 
tions, as well as the respective shares which two or more incre- 
ments of the same cause may have in producing a result. 
Newton, wishing to know how far an ivory ball suspended by 
a cord and allowed to strike a hard surface, would rebound by 
the force of its own elasticity, first of all caused it to swing 
freely in the air, and measured the loss of motion produced by 
the resistance of the air during each vibration. Then adding 
to the length of the rebound the loss of distance incurred in 
the half- vibration of equal length, he obtained the entire effect 
of the elasticity. The observation by astronomers that the 
planet Uranus was sometimes retarded and sometimes accel- 
erated in its orbital course, so as not to be in its calculated 
positions, led to the discovery of the planet Neptune, as the 
cause of the aberrations. So also the fact that comets gener- 
ally do not return from their distant journeys till after the 
expiration of the predicted time, has suggested the existence 
of some cosmic ether, or other medium, capable of obstructing 
the motion of such bodies. 

The fifth rule explains the " method of concomitant 'varia- 
tions" If a phenomenon which is either continuous or recur- 
rent, varies in a manner to correspond with the variations of 
another phenomenon, these phenomena are connected through 
some law of causational sequence. The mere concomitance of 
the variations does not indicate the specific mode in which the 
phenomena are related to each other. It does not, for example, 
show which is cause and which effect, or whether both are effects 
of the same cause ; but the nature of the specific relation is com- 
monly easily determined. When quicksilver was observed to 



Chap. XVI.] INDUCTIVE REASONING. 149 

expand in proportion to the heat about it, no one hesitated to 
believe that heat is the cause of the expansion. So friction 
is proved to be the cause of heat, when it is found that heat is 
evolved exactly in proportion to the amount of force expended 
in rubbing one substance against another. 

The law of concomitant variations is a specific application 
of the principle that every cause and its effect mutually cor- 
respond — the presence or absence of the one involving the 
presence or absence of the other. But it enables us to inter- 
pret a peculiar class of cases, in which the cause never ceases 
from operation ; and in which, therefore, the ordinary method 
of difference is not available. The fact that the tides follow 
the moon, and that the high tides attend the conjunction of 
sun and moon, indicates that the rising and falling of the 
ocean results from the attraction of these bodies. The seasons 
evidently result from the sun's changes in latitude. A corre- 
spondence in the periodical prevalence of " magnetic storms," 
of the Aurora Borealis, and of solar spots, with certain recur- 
rent positions of the planets Jupiter, Saturn, Venus and Mars, 
has led some to think that these planets are the prime movers 
in a remarkable set of meteoric phenomena. 



150 THE MODALIST. [Chap. XVIL 



CHAPTER XVIL 

HYPOTHETICAL AND DISJUNCTIVE REASONINGS. 

1. Inference is also actualistic or hypothetical. 2. The so-called hypo- 
thetical syllogism is translative. 3. The law of logical transfer. 4. Trans- 
lative inference is either express or implicit. 5. The simple hypothetical, 
or translative, syllogism has two modes : (a) the ponendo ponens, (6) the 
■tollendo tollens. Both explained. 6. Logical disjunction is a complicated 
style of hypothetical inference founded on either (a) contrariety or 
(&) contradiction. 7. Contrariety explained. 8. It is the ground of the 
weak disjunctive syllogism; which has one mode, the ponendo tollens. 
9. Contradiction is either categorical or consequential. 10. Two contraries 
become contradictories when the non-reality of either involves the reality 
of the other. 11. Only a pair, not a series, of things can be mutually 
contradictory. 12. The strong disjunctive syllogism has two modes, the 
ponendo tollens and the tollendo ponens. 13. The dilemma is an hypo- 
thetical syllogism, with a plural "major" and a disjunctive "minor." 
It is either (a) constructive or destructive, (If) simple or complex. 

1. With reference to the mode of its sequence, inference is 
either apodeictic or problematic ; with reference to its depend- 
ence on previous perceptions of logical connection, it is either 
orthologic or homologic ; and with reference to the character 
of the conviction produced, it is either actualistic or hypothet- 
ical. Actualistic inference is founded on what is known or be- 
lieved to be fact ; and its consequent is accepted as fact, either 
absolutely or possibly or probably, according to the modality of 
the sequence. Hypothetical inference rests on mere supposi- 
tion, and asserts only what would certainly or possibly or prob- 
ably be fact provided the antecedent were a reality. 

Every hypothetical proposition is illative, or inferential, in 
its nature. This is especially evident in the case of fully 
expressed hypotheticals. "If chlorine be a gas, it is elastic," 
asserts that a certain consequent must be true if a certain 
antecedent be true. The only difference between an hypothet- 



Chap. XVIL] HYPOTHETICAL SEASONING. 151 

ical proposition and an hypothetical inference is that the for- 
mer emphasizes the consequent rather than the antecedent;, 
while the inference dwells equally on both. 

2. That form of reasoning, however, which logicians style 
the "hypothetical syllogism," should not be confounded with 
mere hypothetical inference. It is really an hypothetical 
inference with an addition which has the effect of depriving the 
process as a ivhole of its hypothetical character. When the 
statement, " If chlorine be a gas, it is elastic," is followed by 
the assertion, " chlorine is a gas," the object of this addition is 
to assert the reality of the antecedent, and thereby to change 
the character of the inference from hypothetical to actualis- 
tic. This appears in the conclusion, when we assert, for a 
fact, that "chlorine is elastic." 

In consequence of the application of the term " hypotheti- 
cal " to syllogisms of this kind, some ambiguity arises when 
this adjective is used with reference to inferences generally. 
Were a special name desired for inferences and arguments 
purely hypothetical and unchanged by actualistic addition, 
they might be distinguished as suppositive. The following* 
would be suppositive inferences : " If air be a substance, then 
it occupies space ; if trees spring from seeds, then these trees 
do so ; if all gases are elastic, and oxygen is a gas, then oxygen 
is elastic." These inferences would become "hypothetical" 
syllogisms, if additions were made to them asserting that 
their premises set forth reality. 

3. The law according to which an hypothetical is changed 
into an actualistic inference is a very simple one, and may be 
considered a corollary, or supplementary part, of the general 
law of antecedent and consequent. It recognizes the differ- 
ence between two radical modes of conviction, and operates 
whenever we apply hypothetical statement to actual fact. 
Asserting the reality of the antecedent, it claims reality for 
the consequent. This law might be styled the principle of 
logical transfer, becauses it enables us to transfer an assertion 
from one kind of conviction to another ; and syllogisms whose 
antecedents are constructed in accordance with this principle, 
might be called translative reasonings, or inferences. 



152 THE MODALIST. [Chap. XVII. 

4. The working of this law, may be either express or im- 
plicit. Its express operation occurs when the minor premise, 
as it is called, asserts fact immediately and exclusively. This 
takes place in all translative reasonings concerning existing 
individuals ; as, for example, in the syllogism, " If Socrates be 
virtuous, he merits esteem ; he is virtuous ; therefore he mer- 
its esteem." The implicit working of the law appears when 
the reasoning immediately concerns general objects, or logical 
classes. In saying, " If oxygen be a gas, it is elastic : oxygen 
is a gas ; therefore it is elastic," the minor premise has an 
actualistic force; yet not simply and directly, but only as 
implicated with a general truth. In other words, the assertion, 
" oxygen is a gas," has a double significance ; first, it presents 
a principle which applies, not only to existing oxygen, but to 
any that ever may exist or may have existed ; and secondly, 
it contains the implication that some oxygen actually exists 
and is a gas. The "hypothetical," or translative, syllogism 
depends on this assertion, in the second premise, of the reality 
of the antecedent supposed in the first premise ; and only 
accidentally uses a general truth or principle for this purpose. 
The proper force of general principles in reasoning will be 
considered hereafter, in connection with syllogisms of another 
nature. 

Some define the hypothetical syllogism as that mode of 
reasoning which is governed by the principle of antecedent 
and consequent ; and say that other modes of reasoning follow 
other principles. Though this is not true, we must allow that 
the translative inference is specially related to the generic law 
of inference; inasmuch as the law of logical transfer is not 
only, like other principles, subordinate to the law of reason 
and consequent, but pertains to the operation of that law. 

5. The law of reason and consequent works in two ways ; 
we either assert the consequent with the reason, or we deny the 
reason with the consequent. Hence, also, the law of logical 
transfer has a double operation. That is to say, after an infer- 
ence has been made hypothetically, we may then either assert 
the reason or deny the consequent actualistically, and there- 
upon assert the consequent or deny the reason actualistically. 



Chap. XVII.] HYPOTHETICAL REASONING. 153 

Here we must determine exactly what is meant by asserting 
and denying ; for it might be supposed that assertion always 
signifies the setting forth of something as existing, and denial 
the setting forth of something as non-existent ; whereas the 
terms have wider meanings. Ordinarily we infer from one 
positive fact to another, that is, from one case of existence to 
another. But, in addition to this, we infer from existence to 
non-existence, from non-existence to existence, and from non- 
existence to non-existence. There are, therefore, four styles 
of inference ; which may be illustrated, as follows : " If the 
man has consumption, he will soon die," (from existence to 
existence) ; "if the formation be granite, it does not contain 
coal," (from existence to non-existence) ; "if there be no food, 
we must suffer hunger," (from non-existence to existence) ; 
u if there be no fuel, there can be no fire," (from non-existence 
to non-existence). Now to assert the antecedent or conse- 
quent in any of these inferences is to present it as a reality, 
whether it be a fact of existence or a fact of non-existence ; 
and to deny the consequent or the antecedent is to deny its 
reality, whether that be the denial of existence or of non- 
existence. 

In order to express technically those wide conceptions which 
we have now explained, logicians sometimes call the assertion 
of the antecedent, and that of the consequent which it in- 
volves, the " positing," or " placing," of a statement of fact ; 
and they have termed the denial of the consequent, as well as 
that of the antecedent, the "sublation," or taking away, of a 
statement of fact. They also name that form of inference 
which depends on the " placing " of the antecedent the " modus 
ponendo ponens" or more simply, the "modus poiiens" ; and 
that which follows the sublation of the consequent the "modus 
tollendo tollens" or more simply, the "modus tollens" 

This phraseology has the additional advantage of indicating 
that antecedents arise from assertion and denial, not simply 
because something is asserted or denied, but because, also, 
there is a presupposed subject, or case, or set of circumstances, 
in relation to which the positing or sublation takes place. 

Moreover, as according to the law of contradiction the denial 



154 THE M0DAL1ST. [Chap. XVII. 

of existence involves the assertion of non-existence, and the 
denial of non-existence the assertion of existence \ instead of 
merely denying the consequent, we may, and often do, assert 
its contradictory ; and thereupon deny the antecedent. Hence 
the negative part of the law of logical transfer may assume 
the form, "contradict, or assume the contradictory of, the 
consequent, and you may deny, or contradict, the antecedent." 

6. We have now considered those simple and primary modes 
of " hypothetical " reasoning which are expressed by the ordi- 
nary "conditional syllogism." A more complicated style of 
translative reasoning, which, however, is explainable on the 
same general principles, appears in what are called "disjunc- 
tive " reasonings. 

Logical disjunction is either partial or complete. The first 
exists when it is impossible that two things should be true together, 
so that the placing of either involves the sublation of the other. 
This is the disjunction of contrariety. The second arises when, 
in addition to the foregoing opposition, two things cannot be un- 
true together, so that the sublation of one involves the placing of 
the other. This is the disjunction of contradiction. As con- 
tradiction presupposes contrariety we shall consider the latter 
first. 

7. The nature of contrariety, and its relation to inference 
in general, may be understood from the fact that a case of this 
mode of opposition may be produced by the denial or contra- 
diction of any consequent of necessity. To illustrate this 
point let us take the sequences already mentioned : 

If the man has consumption, he will die soon ; 
If there be no food, we must suffer from hunger ; 
If the formation be granite, there cannot be coal in it ; 
If there be no fuel, there cannot be any fire. 

The first two of these are sequences of positive necessity, the 
one with an antecedent of existence, the other with an ante- 
cedent of non-existence ; the second two are inferences of neg- 
ative necessity, one having a positive and the other a negative 
antecedent. If now we deny, or take the contradictory of, the 
consequent in each sequence, retaining the antecedent un- 
changed, we shall have the following pairs of contraries : 



Chap. XVII.] HYPOTHETICAL SEASONING. 155 

Consumption — continued life ; 
No food — no suffering from hunger ; 
Granite — coal in the formation ; 
No fuel — fire. 

Assert any one of these contraries, and you must deny, or con- 
tradict, its fellow. If the man have consumption, he cannot 
have continued life ; and if he have continued life, he cannot 
have consumption : if we have no food, we cannot be without 
suffering from hunger, but must suffer from that cause ; and if 
there be no suffering from hunger, we cannot be without food, 
but must have a supply : and so on with the other contraries. 
In general, therefore, we say that anything and the contradic- 
tory of any necessary consequent of it, are contraries. The reason 
for this is that the consequent of a necessitating antecedent is 
a condition of that antecedent. Evidently, it is impossible for 
a thing to exist while the contradictory (or any contrary) of 
any of its conditions exists ; or for any contradictory (or con- 
trary) of a condition to exist while the thing conditioned exists. 

The perception of contrariety, however, does not depend on 
a previous perception of necessary sequence ; indeed, it com- 
monly takes place independently. For two things may be 
directly perceived to be of such a nature that the existence of 
one of them conflicts with, that is, involves the non-reality of, 
some condition of the other ; in which case they are, and must 
be, contraries. This incompatibility of one thing with others is 
as much a part of the nature and constitution of things as the 
compatibility of one thing with others is, and may be as directly 
perceived. For example, it is as immediately evident that two 
bodies cannot occupy the same space at once, and that if the 
one is there the other is not there, as that a body must occupy 
some space, or that it may occupy any sufficient space which 
would be otherwise unoccupied. 

Contrariety is especially noticeable when a number of na- 
tures, or things predicable, which have a common character, 
have also such peculiarities that no two of them can belong to 
the same individual subject. Hence the co-ordinate species in a 
correct logical division are contraries one to another with refer- 
ence to their inherence in the same subject. For instance, 



156 THE MODALIST. [Chap. XVII. 

if an object is of any one color, say red, it cannot be of any 
other color at the same time ; if a triangle be isosceles it 
cannot be equilateral or scalene, or if it be equilateral it cannot 
be isosceles or scalene. 

8. The inference of contrariety can be expressed in the 
same way as "conditional," or simple hypothetical, inference, 
but it differs from the latter in the peculiar indirectness with 
which the sequence is conceived. The consequent of simple, or 
ordinary, hypothetical sequence is immediately conceived and 
asserted as true; that of contrary inference is obtained by 
conceiving first of something and then of the immediate, or 
categorical, contradictory of that something, and is the asser- 
tion of this contradictory. Conceiving of " red " as a contrary 
of "white," and then of its contradictory, "not red," we say 
that, if the paper is white, it is not red. Contrary inference, 
also, has a doubleness, because each contrary may be, and com- 
monly is, conceived of as being, in its turn, antecedent to the 
non-reality, or to the immediate contradictory, of the other. 

This doubleness may be expressed with any pair of con- 
traries, if we follow the formulas, " A cannot be both B and C ; 
it is B; therefore it is not C," and "it is C; therefore it is 
not B." " The triangle cannot be both equilateral and scalene ; 
it is equilateral ; therefore it is not scalene," or " it is scalene ; 
therefore it is not equilateral." 

Argument of this form may be distinguished as the weak 
disjunctive syllogism. It admits only the "ponendo tollens" 
The ordinary, or strong, disjunctive syllogism, as we shall soon 
see, has a " modus ponens" as well as a " modus tollens." 

9. This brings us to that thorough-going form of disjunc- 
tion which is technically called " contradiction." For contra- 
dictory opposition includes contrariety and something more. 

First, then, we say, negatively, that the disjunction of con- 
tradiction is not at all limited to that opposition which is based 
on the law of contradiction and excluded middle. This law 
relates to any pair of propositions which set forth the exis- 
tence and the non-existence of the very same thing ; and asserts 
that if one of them be true the other is false, and that if one 
be false the other is true. The contradictories of which we 



Chap. XVII.] HYPOTHETICAL REASONING. 157 

have made mention above are of this sort. But contradictory 
inference in general is chiefly occupied with propositions which 
set forth the existence or non-existence of tivo different tilings ; 
and asserts the falsity of either of these propositions because 
of the truth of the other, or the truth of either because of the 
falsity of the other. To account for such inference we must 
assume, not merely the law of contradiction, but also an operation 
of the general law of antecedent and consequent additional to 
that which appears in immediately self-evident contradiction. 

Those propositions which set forth the existence and the 
non-existence of the very same thing, may be styled categorical 
contradictories ; for this adjective sometimes indicates that a 
statement is absolute, or unaccompanied by any reason. Such 
statements as " the man is guilty " and " the man is not 
guilty," are categorical contradictories ; because their opposi- 
tion, though founded on reason, takes place according to a law 
of whose operation the mind is scarcely conscious. The reason 
for such contradiction is considered only by logicians ; it is the 
"law of Contradiction." But those propositions which set 
forth two different things or natures which conflict with each 
other both as to existence and as to non-existence, may be called 
consequential contradictories; for their opposition is asserted by 
the mind on account of some specific reason in the nature of 
the things considered. In the case of any collection of units 
that the number of them should be odd, and that it should be 
even, are contradictories consequentially related to the nature 
of odd and even integral numbers. 

10. Secondly, we say, positively, that any two contraries 
become the contradictories of one another ivhen the circum- 
stances of the case are such that the non-reality of either is the 
only condition wanting to complete an antecedent necessitating the 
reality of the other. Evidently in any case the non-reality of 
either of two contraries is a condition of the reality of the 
other. Let this now be the only condition needed ; thereupon 
the two contraries are contradictories. For whenever the non- 
reality of a first thing necessitates the reality of a second, the 
law of " the denied consequent " requires that the non-reality 
of the second must also involve the reality of the first. 



158 THE MODALIST. [Chap. XVII. 

In the case of a plane triangle there are three contraries ; it 
may be either equilateral, or isosceles, or scalene. If now we 
limit the case to triangles which have at least two sides equal, 
only two contraries remain; and these are contradictories. 
For every triangle with at least two sides equal is either 
equilateral or isosceles. In general when a case of necessary 
consequence admits of two, and only two, alternative conse- 
quents, these become contradictories. If a house is certainly 
to be painted, and only two colors are obtainable, say brown 
and white, these are contradictories of each other. 

11. Several things may be contradictory to one and the same 
thing. In a quadrilateral both the inequality of opposite sides 
and the inequality of opposite angles, are contradictories of 
its being a parallelogram. But things contradictory of one 
and the same thing cannot be contradictories of each other. 
For, being contradictories of one and the same thing, they 
must all be non-existent together if that thing exist; but 
things contradictory of each other cannot be non-existent 
together. Neither can the contradictories of one and the 
same thing be the contraries of one another: for they must 
all exist together if their common contradictory do not exist. 
Therefore we cannot have a series of mutual contradictories ; 
as we can of mutual contraries. We must deal with contra- 
dictories in pairs. a 

The relation of contradictory to direct inference may be 
illustrated by the fact, that contradictory conceptions may 
always be found when two things are exact logical necessi- 
tants of each other. For either of such necessitants and the 
categorical contradictory of the other, are related to each 
other as consequential contradictories. To exemplify this, 
let smoke and fire involve the existence of each other, and 
the non-existence of either the non-existence of the other; 
then " smoke " and " no fire," or " no smoke " and " fire," are 
mutually contradictory. If we assert either we deny the 
other, and if we deny either we assert the other. The con- 
ception of contradictories, however, need not be based on that 
of necessitants ; contradiction, like contrariety, can be per- 
ceived directly. 



Chap. XVII.] HYPOTHETICAL REASONING. 159 

Moreover, as contrariety is specially noticeable between the 
species of the same genus, that is, between the specific forms 
of the same generic nature, so the most prominent mode of 
contradiction arises when a genus consists, or is made to con- 
sist, of only two species. In the case of integral numbers to 
be odd and to be even are natural contradictories ; while to be 
odd and to be a multiple of four, are merely contraries. But 
should a collection of numbers contain only odd numbers and 
multiples of four, in that case, and with reference to the mem- 
bers of that arbitrary class, to be odd and to be a multiple of 
four would be contradictories. 

12. When translative reasoning is based on the relations of 
contradiction, it is commonly expressed by the strong "dis- 
junctive syllogism." This consists of a major premise, setting 
forth the two contradictories in their double hypothetical 
opposition to each other ; of a minor premise, in which one of 
the contradictory conceptions is actualistically asserted or 
denied ; and of an actualistic conclusion. We say, " The line 
is either straight or bent," and then "it is straight, therefore 
it is not bent " ; or " it is not straight, therefore it is bent " ; 
or "it is bent, therefore it is not straight" ; or "it is not bent, 
therefore it is straight." The disjunctive major premise is 
really a condensed statement of four hypothetical propositions ; 
the minor actualistically asserts one of the four antecedents of 
those propositions ; the conclusion is the consequent of that 
antecedent. 

Evidently contradictory inference has two modes, the "po- 
nendo tollens" and the " tollendo ponens" : contrary inference 
has only one, the "ponendo tollens." There is, however, a 
style of reasoning which might be called that of contradic- 
tory contrariety, in which, while dealing with contraries, we 
can regard them to some extent as contradictories ; and can, 
therefore, use the "tollendo ponens" mode of argument, as 
well as the "ponendo tollens." This arises ivhenever the con- 
traries in any given case are enumerated exhaustively ; and espe- 
cially when a complete division is given of some existing genus. 
For instance, if we say, " The season was either spring, sum- 
mer, autumn or winter," we not only can assert any one 



160 THE MODALIST. [Chap. XVIL 

contrary and deny each of the rest, but, if we deny all the rest, 
we can assert that one ; or, if we deny some and leave some 
undenied, we can assert these last disjunctively. For, if it is 
neither spring nor summer, it must be either autumn or winter. 

In the syllogism, " The man is either a knave or a fool ; he; 
is not a knave, therefore he is a fool," the " tollendo ponens " 
holds good, although the major premise does not explicitly 
enumerate the contraries. The reason is that the conclusion 
is supported by a suppressed and understood contrary, the- 
complete enumeration being, " The man is either a knave or a 
fool or both." We cannot, however, say, " The man is a knave, 
therefore he is not a fool," using the "ponendo tollens" ; 
because the suppressed contrary does not support this con- 
clusion. We see, therefore, that in every case of tollendo 
ponens, notwithstanding this apparent exception, all the alter- 
natives are and must be considered. For in the foregoing 
instance the "tollendo ponens" is justified and the "ponendo 
tollens " condemned only after consideration of the suppressed 
alternative. 

13. A complicated form of argument involving both direct and 
disjunctive hypothetical inference has been called the dilemma, 
or double assumption. Its major premise assumes two or more 
sequences as hypothetically true. Its minor premise is actual- 
istic, and either asserts the antecedents of those sequences dis- 
junctively, or denies their consequents disjunctively : in the- 
former case the dilemma is " constructive " ; in the latter, 
" destructive." The conclusion either asserts the consequents 
disjunctively, unless there be only one common consequent, 
in which case that is asserted; or it denies the antecedents 
disjunctively, unless there be only one common antecedent, in 
which case that is denied. The reasons for these operations 
are apparent from the nature of hypothetical and disjunctive 
inference. The constructive dilemma is either complex or 
simple, according as the sequences given in the major premise 
have different consequents or one common consequent ; and, in 
like manner, the destructive dilemma is complex or simple, 
according as the given sequences have different antecedents, 
or one common antecedent. 



Chap. XVII. ] HYPOTHETICAL BEASONING. 161 

The following is a complex constructive dilemma : 

" If a statesman who has discovered his policy to be mistaken, alters 
his course, he is chargeable with inconsistency ; and if he do not alter it, 
he is guilty of deceit. 

But he either does, or does not, alter it ; 

Therefore he must be either chargeable with inconsistency or guilty of 
deceit." 

The following is a simple constructive dilemma : 

"If a study furnish information, it should be pursued; and if it 
develop the mind, it should be pursued. 

But this study either furnishes information or develops the mind ; 
Therefore it should be pursued." 

The following is a complex destructive dilemma : 

" If the man were wise, he would not speak irreverently of Scripture 
in jest ; if he were good, he would not do so in earnest. 
But he does it either in jest or in earnest ; 
Therefore he is either not wise or not good." 

The following is a simple destructive dilemma : 

"If the man were wise, he would not speak irreverently of Scripture 
*n jest ; neither would he do so in earnest. 
But he does it either in jest or in earnest ; 
Therefore he is not wise." 

In these last arguments it will be noticed that a negative 
consequent is denied by giving its contradictory; which is 
positive. 



162 THE MODALIST. [Chap. XVIII. 



CHAPTER XVIII. 

PROBABLE INFERENCE. 

1. The tychologic principle. 2. Chances. 3. Their individuality. 
4. Their arithmetical value. 5. Their addition and subtraction. 6. Their 
multiplication and division. 7. Compounded probability explained. 
8. The compounding of a series. 9. The addition of compounded proba- 
bilities. 10. The application of the binomial formula to probabilities 
connected with recurrent trials. 11. Philosophical probability and im- 
probability. 12. Probability may be either orthologic or homologic. 
13. Analogical and inductive probability. 14. Moral certainty. 

1. Probability attaches primarily to single inferences and 
to illative propositions as the expression of these inferences ; 
after that, and in consequence of that, it may affect syllogisms, 
or those inferences which follow upon the composition of 
propositions. For if either premise of a syllogism be probable, 
the conclusion must be probable. If we can understand the 
nature of the single probable inference, no difficulty will be 
experienced respecting that of probable reasoning. 

We find the radical law of all probable inference in the 
principle of " the ratio of the chances " ; which principle may 
be named the tychologic principle. 

2. The nature of " chances " is best explained by consider- 
ing them, in the first instance, as conflictive consequents of 
possibility, and as making up a family, or company, of such 
consequents. The antecedent of an inference in possibility 
differs from the antecedent of an inference of necessity in that 
the latter cannot have conflictive consequents, while the former 
may. If a thing be necessary, nothing that cannot exist along 
with it can also be necessary. But two or more things may be 
possible at the same time, even while no two of them can be 
actual together. When we know simply that a book is a 
bound volume, we can say that it may be a quarto, or an 



Chap. XVIII. ] PROBABLE INFERENCE. 163 

octavo, a duodecimo, or of some other style ; but if it be any 
one of these, it cannot be any of the others. The fact that it 
is a bound volume is an antecedent of contingency, or pos- 
sibility, with a number of connective consequents. Now, when 
a case admits of only a limited number of connective conse- 
quents, one of which must be realized, and when it presents no 
ground for believing that any one of them, rather than any 
other, has been, or will be, realized, we call the consequents 
" chances." 

The relation between a chance and a consequent of necessity 
is such that the former changes into the latter whenever the 
antecedent of contingency is filled out, in any way, so as to 
make it an antecedent of necessity. Should we know not only 
that a volume is bound, but also that it is a copy of a book 
published only as a quarto, then we would say that the vol- 
ume must be — not that it may be — a quarto. But, although 
chances are thus related to necessary consequents, they them- 
selves are never necessary, or real, but only ideal, objects. 
When a chance is realized it ceases to be a chance ; and its 
companions, also, cease to be chances in their failure to be 
realized. 

3. Every chance is conceived of as an individual, and not as 
a general, consequent of contingency. Should a drawing take 
place from a box containing twenty black, thirty red, and fifty 
white marbles, there would be three general consequents of 
contingency, viz., that a black, that a red, and that a white 
marble, should be drawn. These general consequents would 
not be chances according to the logical use of language. A 
chance in the foregoing case would be the possible drawing of 
any one ball ; and evidently there would be one hundred such 
possibilities. In determining the " ratio of the chances " we 
always conceive of these individual and equal possibilities. 
We cannot, however, always conceive of them as directly and 
as definitely as in the case just considered. 

If a postman called at a certain house to deliver letters 
about four days out of every thirty, one might say at first that 
on any given day there are only two chances, viz., that he may, 
and that he may not, call. But properly these are two general 



164 THE MODALIST. [Chap. XVIII. 

events — or rather two events of a general character — each of 
which is supported by a number of chances. The case pre- 
sents thirty chances — or individual possibilities of equal cred- 
ibility. According to four of these the postman will call; 
according to twenty-six he will pass by. These chances may 
not be definitely conceived of in our judgment respecting the 
likelihood of a call ; but they are the real rational basis for 
such a judgment. 

The individuality of the chances means little more than 
that they are the units of measure among which the confi- 
dence of the mind is equally distributed. In every case of 
probability there is a necessity that one of the chances should 
be realized, and, as we have no reason to expect one more than 
another, we expect each equally, dividing among them the con- 
fidence of certainty. 

4. In order to indicate the value of a single chance mathe- 
matically we must employ a fraction wJiose numerator is unity 
and whose denominator is the whole number of chances. In the 
case of the postman the value of each individual chance is one- 
thirtieth of certainty, while the two general events supported 
by the chances have the values -^ and -§£, or -f^ and ||. The 
application of mathematical methods to the determination of 
probabilities begins with this employment of fractions ; and it 
leads to the addition, the subtraction, the multiplication and 
the division, of fractions representing degrees of probability. 

5. When two or more events are specific forms of the same 
general event, so that, if either of them happen, that will be 
a happening of the general event, the probability of the gen- 
eral event is found by adding the probabilities of all the speci- 
fic events included under it. Should a cubical die whose sides 
are numbered from 1 to 6 be thrown out of a box, the chance 
for any one number appearing uppermost is i, and the proba- 
bility for the appearance of an odd number would be f, this 
being the sum of the chances for the three sides bearing the 
three odd numbers. 

But were the die thrown twice, we could not say that the 
probability for an odd number appearing on both throws would 
be £ -f- f , or unity ; for " an odd number on both of two 



Chap. XVIII.] PROBABLE INFERENCE. 165 

throws" would not be a general event possible in either of 
two specific forms, but a double event rendered possible by a 
doubled antecedent. We shall see that the probability of such 
an event is found by multiplication, not by addition. 

Conversely, if an urn contain 30 white balls, and 70 colored 
red or otherwise, the probability for the drawing of a colored 
ball is t 7 ¥ °q-. And if fifty of these 70 chances favor other colors 
than red, the probability for a red ball must be y 7 -^- — -££$ or 

m «» \. 

The foregoing examples illustrate the only cases in which 
the determination of probabilities calls for, and admits of, the 
addition and subtraction of fractions. These operations are 
applicable only when some general event and its specific forms 
are all conceived of as consequents of the very same antece- 
dent of contingency. 

6. The multiplication of probabilities — that is, of fractions 
indicating probability — is used when one consequent of contin- 
gency, in other words, one probable event, is consequent upon 
another. By means of this multiplication we determine the 
probability of the compound event which would be composed 
of both the probable events in case they should happen ; which 
also is the probability of the conclusion, or of any other part y 
of this compound event, as part of it. If there be one chance 
in five that a certain criminal will be caught, and one in three 
that he will be convicted after being caught, it is plain that 
now, and until he may have been caught, the probability of 
his conviction will not be one-third of certainty — for that 
would involve the assumption that he certainly has been 
caught, or shall be — but only ^ of ^, or ^ ; which also is the 
probability of the entire compound event of his being both 
caught and convicted. Therefore the probability of a com- 
pound event, or of any part of it as such, is the product of the 
probabilities of its component events. 

Conversely, if we know both the probability of an event 
compounded of two probable events and the independent prob- 
ability of one of its components, and if we divide the prob- 
ability of the event by the probability of that component, we 
shall obtain the independent probability of the other compon- 



166 THE MODALIST. [Chap. XVIII. 

ent. If we know that the probability of a criminal being both 
captured and convicted is ^ z , and the probability of his being 
caught is jr, we can say that the probability of his being con- 
victed, in case he is captured, will be |-. Because ^ divided 
by -1- is equal to i 

7. In the foregoing illustration the events composing the 
compound event are related to each other as the condition of 
a result and the result conditioned. Such a relatedness, how- 
ever, is not necessary in order to a compounding of probabili 
ties. Any two events which are not of repugnant natures, and 
which, therefore, may both be realized, may be conceived of as 
one double event. The event of ace on one throw of a die, 
with the probability -§-, and that of head on one toss of a 
penny, with the probability J, may be compounded into the 
event "ace on one throw and head on one toss," with the 
probability -jL. It is evident, moreover, that, after two events 
have been compounded, a third may be compounded with the 
result ; and that, in this way, any number of events may be 
made to compose an event whose probability is the product of 
the probabilities of its parts. 

8. An interesting case of compounded probability occurs 
when the component events may be successively expected 
according to a regular series of fractions. After the shuffling 
of a complete pack of playing cards, the probability of a pic- 
tured card being uppermost is -J-f, there being 52 cards in all, 
and 12 of these pictured. Then, should this event take place, 
and the pictured card be laid aside, the probability that the 
next card will be found to be pictured will be -J^-. If this 
event occur and the second pictured card be laid aside, the 
probability for the appearance of a third will be -J-J. And, if 
the subsequent drawings continue to yield pictured cards, the 
series will go on till only one such card remains in the col- 
lection ; and will terminate with the fraction J y , the probability 
for that card. Such being the separate probabilities for the 
successive appearances of pictured cards, that for a combined 
event can be easily determined. For example, the probability 
that the first three cards will be pictured must be the product 



Chap. XVIII. ] PROBABLE INFERENCE. 167 

of the first three fractions of the series. That is |f • £i • £$-, or 
1 1§ 1 8 o ^ or a little less than one in a hundred. 

But the probability that the first card will be pictured, the 
second plain, and the third pictured, will be the product ^f • 
|-2- • ii or xfHro or a k oi rt ■£%. This would be the result also 
if the plain card were to be expected first, or last, of the three. 

When the compounded probabilities are not a variable series, 
but equal to each other, as happens when precisely the same 
trial, or antecedent of probability, is repeated, the calculation 
is simpler. For instance, the probability that a pictured card 
will be uppermost three times in succession after three shuf- 
flings of the entire pack, would be found by raising the frac- 
tion ^f- to its third power. It would be 2 ^ 7 , or more than 
one in one hundred. 

9. A more complex class of problems than those hitherto 
noticed calls for both the multiplication and addition of proba- 
bilities. For addition is used whenever the probability of a 
general event is to be determined by uniting the probabilities 
of its specific forms. 

Let the question concern the probability of obtaining " ace 
on two successive throws " of a die. This question is ambigu- 
ous; it may concern (1) the probability of "ace on both 
throws," or (2) that of "ace on one throw only," or (3) that 
of " ace on one throw at least," perhaps on both. In the first 
of these events, " ace on both throws," the second throw, by 
which the event may be completed, is not to be allowed unless 
the first throw is successful. We therefore compound the 
separate probabilities of these two throws, that is, we multiply 
i by i and find the probability required, ■£$. This calls for 
no addition of fractions. But the event "ace on one throw 
only" may take place in either of two ways; for ace may 
appear on the first throw only, or on the second throw only ; 
and the probability of it must be determined by adding to- 
gether the probabilities of its specific forms. The probability 
of ace on the first throw and not on the second is i • £, or ^. 
That of ace not on the first throw but on the second is f • £, 
or 3 5 g. Adding these together we find the probability sought 
for, if or T \. Finally, the chances for " ace on one throw at 



168 THE MODALIST. [Chap. XVIII. 

least " (out of the two) comprise those of three possible events, 
viz. of "ace on first throw only," of "ace on second throw 
only," and of "ace on both throws." We have just seen that 
the united probability of the first two of these events is T 5 F . 
Add to this g 1 ^, the probability of ace twice in succession, and 
we have ^ as the probability of ace once at least in two 
throws. 

10. An ingenious theorem respecting recurrent probabilities 
provides for the calculation of the chances for an event happen- 
ing any given number of times, in any given number of trials. 

Let an urn contain any number of balls, one third of them 
being red, and the rest of other colors. The probability 
that the first ball drawn out by a blindfolded person will be 
red is -| ; the probability that it will not be red is -§. More- 
over, if every ball drawn out be immediately replaced, these 
same probabilities will recur with every subsequent trial. We 
may now ask " What is the probability of a red ball appearing, 
say, 4 times, and failing to appear 6 times, in 10 consecutive 
trials ? Or of its appearing 7 times, and failing to appear 3 
times ? " Such questions can be easily answered by the use 
of a mathematical formula. 

Let us designate the event, the recurrence of which an exact 
number of times in a given number of trials is the 'subject of 
enquiry, by E, and its failure to occur by F, the probability 
of its occurrence on one trial by p, and the improbability of 
its occurrence on one trial by q. Then, on two trials, the possi- 
ble combinations are the following double events : first, EE, 
with the compound probability p xp, or p 2 ; FF, with the 
probability q x q, or q 2 ; EF, with the probability p x q, or pq ; 
and FE, with the probability q xp, or qp, or pq. Evidently 
no other combination than these is possible. Moreover, EF 
and FE, as they are alike constituted by one success and one 
failure, may be considered as varieties of that general com- 
pound event in which we conceive of one event and one failure 
without respect to order of occurrence. The probability of that 
event, therefore, will be pq+pq, or 2pq, this being the sum 
of the probabilities of the specific events. If, now, we drop 
either the designation EF or FE and use the other (say EF) 



Chap. XVIII. ] PROBABLE INFERENCE. 169 

for that general event which covers both EF and FE, we shall 
have only three possible events, EE, EF, and FF, with prob- 
abilities expressed respectively by the terms of the polynomial 
p 2 + 2pq + q 2 . For example, ^ being the probability for ace 
on one throw of a die, and -J the probability for the failure of 
that event, these values being substituted for p and q in the 
foregoing polynomial, the several terms give the probabilities 
for ace twice on two throws, EE ; for ace once only on two 
throws, EF; and for failure of ace on both throws, FF. 
Thus - (i) 2 + 2 (J X f ) + (f Y, or ^ + if + M- 

It should be noticed that the sum of these fractions is unity, 
or one ; as it ought to be. For, since one or other of the three 
events must happen, they divide between them all the chances 
in the case. 

Should we now make three trials, instead of two, the pos- 
sible compound events, with their probabilities, will be as 

follows : 

EEE with the probability ppp =p B 



EEF » « 


' ppq =p* q 


EFE " " ' 


' pqp=p 2 q 


FEE " " ' 


' qpp=p 2 q 


EFF " " ' 


pqq =pq* 


FEF " " ' 


' qpq=pqz 


FFE " " t ' 


qqp=pq 2 


FFF " " ' 


qqq = g 3 . 



Again disregarding the order in which the component events 
may occur, these eight compound events may be conceived of 
as four, namely, EEE, EEF, EFF, and FFF; and, evidently, 
the probabilities of these four events are expressed by the 
terms of the polynomial, p z + 3p 2 q + 3pg 2 + q s . This is the 
cube, just as the polynomial first obtained was the square, of 
the binomial p + q. In like manner the development of this 
binomial to its fourth power, will give the different probabili- 
ties that an event with the separate probability, p, will occur, 
on four trials, every time, or only thrice, or only twice, or 
only once, or not at all ; — the antecedent of probability 
being exactly repeated in every trial. And, in general, the 
development of p + q to the nth power will give all the prob- 
abilities of the occurrence of an event any number of times on 



170 THE MODALIST. * [Chap. XVIII. 

n trials; p being the probability, and q the improbability, of 
the event on one trial. For instance, in order to determine 
the chances for " ace three times only in ten throws," we must 
raise p -f q to the 10th power, and then find the numerical 
value of the term whose literal part is p 3 g 7 , after substituting 
i for p and -f for q. 

The foregoing theorem belongs to a department of mathe- 
matics in which men of genius have discussed many interesting 
problems, and which may be taken as a proof that problematic 
inference is no less rational in its methods, and no less con- 
nected with the necessary nature of thought and of things, 
than apodeictic inference is. 



In the above discussions the "multiplication" of proba- 
bilities must be taken to mean their multiplication one by 
another — the compounding of them. The multiplication of 
a probability by a whole number is an operation altogether 
different from this : it is only a short way of adding the equal 
probabilities of two or more possible specific results, connected 
with one and the same antecedent, and whose united probability 
is that of a more general event. 

11. The calculation of chances brings into prominence a 
wide philosophical use of the words "probable" and "improba- 
ble " ; which it may be well to define. Ordinarily the proba- 
ble is that which has the majority of the chances in its favor ; 
and the improbable is that which only a minority of the 
chances support. According to common speech the same event 
cannot be both probable and improbable under the same cir- 
cumstances. But, philosophically, that is probable which has 
any chances at all in its favor, whether they be few or many ; 
and that is improbable which has any chances at all against it. 
According to these technical meanings the most improbable 
event has some degree of probability, and the most probable 
some degree of improbability. In ordinary language we say 
that " ace on the first throw of a die " is not probable, but 
highly improbable ; mathematically and philosophically, it has 
the probability of one-sixth. 



Chap. XVIII.] PROBABLE INFERENCE. 171 

Probable as well as demonstrative inference may take place 
either orthologically — that is, directly from an antecedent, 
and without reference to any previous case of similar conse- 
quence — or homologically. In this latter case, instead of 
directly estimating chances, we give the consequent of a re- 
peated antecedent the same probability as in a previous judg- 
ment. The instances of probable inference discussed above are 
all orthologic ; but any of them may be the basis for an homo- 
logic inference. 

12. The relation between orthologic and homologic infer- 
ence is precisely the same in problematic as in apodeictic 
sequence ; and does not call for special discussion. Some 
remarks, however, are in place here concerning our probable 
judgments respecting natural laws and events. These all pass 
under the generic name of probable induction, but are often 
divided into two classes, one of which is especially entitled to 
this name, and the other of which is sometimes known as rea- 
soning from, or according to, the analogy of Nature. Probable 
induction, in the specific sense, is essentially a form of prin- 
cipiation ; and takes place when a consequent follows a causa- 
tional antecedent, not invariably, but only sometimes, or for 
the most part. This happens when some power adequate to 
produce a result is occasionally counteracted ; or when some 
tendency which needs advantageous circumstances to render it 
effectual, is only sometimes attended by such circumstances. 
Ordinarily a wound produces pain ; mental excitement or bod- 
ily stupor or rapidity of infliction may prevent this. There- 
fore we only say that a wound is likely to produce pain. 

Three steps may be distinguished in forming this inference. 
We say, first, "Most wounds have caused pain"; then, by 
principiation, " Most wounds produce, or will produce, pain " ; 
and then, by the tychologic principle, that is, according to the 
ratio of the chances, "A wound is likely to produce pain." 
Because any wound, taken at random, may be one of those 
which are painful. But, in the foregoing process, the tycho- 
logical judgment may precede the principiation without any 
change in the result. Thus, having seen that most wounds 
have produced pain, we may say, first, that any one of these 



172 THE MODALIST. [Chap. XYIII. 

observed wounds was probably painful, and then, inductively, 
that any wound whatever is likely to be painful. Ordinary 
judgments of probability are formed in one or other of these 
ways. 

13. The inference from the " analogy of Nature " differs 
from the foregoing in that it is not supported by the same- 
ness, or exact similarity, but only by an imperfect similarity, 
of the new antecedent to that already known to have a certain 
consequent. It is founded on the principle that whatever in 
the natural Universe resembles a known cause, or reason, is 
probably or possibly a true and sufficient reason. Though this 
inference may terminate in principiation it is mainly paradigm- 
atic; it is essentially a reasoning from one parallel case to 
another ; but it is founded on a parallelism which has been 
only imperfectly established; and which, therefore, is only 
probable, or not unlikely. Both the inductive and the analogic 
inference assume confidently that Nature has an intellectual 
unity, and that her methods are fixed and uniform : but in the 
former case a law of natural action has been discovered, while 
in the latter there are only grounds for conjecture. The prob- 
ability of probable induction arises because, though the ante- 
cedent is defined and known, the consequent does not follow 
always, but with exceptions ; that of analogical inference 
arises because the existence of a sufficient antecedent is only a 
matter of probability or of possibility. We cannot be sure 
that other planets or stars are inhabited because our world 
contains the race of Adam ; for the case presents only a prob- 
able or conjectural antecedent. 

14. When the proportion of the chances in favor of any 
event, or course of events, is so great that we feel authorized 
utterly to disregard the chances against it, the event is said to 
be morally certain. Thus the alternation of day and night, 
and of the seasons, and the continued earthly existence of the 
human family, during the coming year, are things of which we 
have no doubt. For the practical purposes of logic this cer- 
tainty differs nothing from the conviction of clear memory, or 
of immediate cognition, or of demonstrative evidence. But it 
is important to remark that the highest probability can never 



Chap. XVIIL] PROBABLE INFERENCE. 173 

really reach absolute certainty. No matter how extreme the 
likelihood of a thing may be — no matter how small the pro- 
portion of the chances against it to the chances for it may be 
— still, so long as a thing is probable, there is a possibility of 
the opposite. Were there a thousand millions of chances for 
an event, and only one against it, that one chance would in- 
volve the perfect possibility of its non-occurrence. 



174 THE MODALIST. [Chap. XIX. 



CHAPTER XIX. 

THE OPPOSITION OF PROPOSITIONS. 

1. Pertains to illative propositions having the same subject and predi- 
cate. 2. Dogmatic assertions may be opposed in quantity and in quality. 
3. Their subalternation and superalternation. 4. Their contrariety. 
5. Their contradiction. 6. Exclusively partitive assertions. 7. Subcon- 
trariety. 8. Summary of the laws of opposition. 9. Modal opposition 
essentially corresponds with dogmatic. 10. Modal contrariety. 11. Modal 
subalternation. 12. Modal contradiction. 13. This last kind of opposi- 
tion involves a specific kind of contingency in the sub-contraries. 14. Modes, 
of contingency or possibility : (a) the embedded, (&) the unstable, or un- 
guarded, (c) the stable, or guarded, (d) the half-stable, or half-guarded.. 
15. This last, as positive and negative, becomes encouraging and dis- 
couraging contingency ; and furnishes the contradictories of necessity and 
impossibility. 16. Sub- contrariety. 17. Probability participates in the 
oppositions of contingency. 

1. Illative propositions are the most important in logic. 
Among illative propositions those which are general, and 
which, therefore, present laws, or rules, of inference, are espe- 
cially important. Logic is so much concerned with these that 
it might even be called the science of " Canonics " ; as it was 
anciently by the Epicureans. 

These general illative propositions, when expressed cate- 
gorically, are of two classes ; first, the pure, or dogmatic, in 
which we make either universal or particular assertions re- 
specting the members of a logical class; and secondly, the 
modal, or conditionative, in which we make either apodeictic 
or problematic assertions respecting a general subject. 

When two propositions of either of these classes have the 
same subject and predicate terms, but differ otherwise, they 
are said to be opposed — immediately opposed, to one another. 
Sometimes, with a restricted use of language, only propositions 
which are contrary to, or contradictory of, each other, are- 



Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 175 

spoken of as mutually opposed. But logicians also charac- 
terize any propositions as being opposed to each other when 
they have the same subject and predicate terms, but differ 
otherwise ; whether they conflict with each other or not. 

The various modes in which propositions may be opposed 
are worthy of study, because, in every opposition, the truth or 
the "falsity of at least one of the opposed propositions can 
be inferred from the truth or from the falsity of the other. 
Let us enquire first concerning the oppositions of pure, and 
then concerning those of modal, categoricals. 

2. Dogmatic categoricals may be opposed in quantity, or in 
quality, or in both. They are opposed in quantity when one is 
universal and the other particular, both being either affirma- 
tive or negative ; in quality when one is affirmative and the 
other negative, both being either universal or particular; in 
both quantity and quality when one is universal and affirma- 
tive and the other particular and negative, or when one is 
universal and negative and the other particular and affirmative. 
The propositions "all men are wise" and "some men are 
wise," as also the propositions " no men are wise " and " some 
men are not wise," are opposed in quantity. The propositions 
" all men are wise " and " no men are wise," as also the propo- 
sitions " some men are wise " and " some men are not wise," 
are opposed in quality. The propositions "all men are wise" 
and "some men are not wise," as also the propositions "no 
men are wise " and " some men are wise," are opposed in both 
quantity and quality. 

For the sake of brevity logicians indicate these different 
forms of opposed propositions by the vowels A E I and : 
A stands for the universal affirmative, E for the universal 
negative, i" for the particular affirmative, and for the par- 
ticular negative. 

The oppositions of these propositions have also been sym- 
bolized by the sides and the diagonals of a square, the corners 
of which have been marked severally by the four vowels. 
In short, the eye is made to help the mind, by means of the 
following figure, which is called "the logical square " : — 



176 



THE MODALIST. 



[Chap. XIX. 



Contrariety 




Sub-contrariety 



Eeference to this diagram will be found to assist the appre- 
hension and the memory. 

3. The opposition of subalternation (which also, from a less 
important point of view, may be termed superalternation) 
exists between A and I and between E and 0. In this oppo- 
sition, according to the common view, the subalternate follows 
if the superalternate be allowed. If "all men are wise," then 
" some men are wise " ; if " no men are wise," then " some 
men are not wise." These are immediate orthologic infer- 
ences ; the law governing them is " Aristotle's dictum," that 
" whatever is true of a class universally, is true of any number 
of its members." But this axiom, does not authorize the con- 
verse inference ; we cannot infer the superalternate from the 
subalternate, as such. We can, however, on the principle of 
the " denied consequent," infer the falsity of the superalter- 
nate from the falsity of the subalternate. 

Here, however, we must add that the relation of subalterna- 
tion may be defined in a way which implies that the subalternate 
cannot be completely and exactly inferred from the superalter- 
nate. This definition is an improvement on the common view 
of subalternation, and will be explained later, in the present 
chapter. 

4. The opposition of contrariety, or confliction, exists be- 
tween A and E. If A be true, E is false ; and if E be true, 
A is false. If " all men are wise," it cannot be that " no men 
are wise " ; and if " no men are wise," it cannot be that " all 
men are wise." This opposition is a consequence of that im- 
mediate contrariety which exists between each superalternate 
and the denial of its subalternate. E immediately involves 



Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 177 

the denial of I, which denial is immediately contrary to A ; 
therefore E involves the denial of A. If " no men are wise/' 
it is not true that " some men are wise " ; and, if it is not true 
that " some men are wise," it is not true that " all men are 
wise." In like manner, A is immediately followed by the 
denial of 0, and the denial of by the denial of E. A and E, 
therefore, are the contraries of one another. 

But E is not the only contrary of A, nor A of E. Each has 
another — a co-ordinate contrary. For A must be false if only 
be true, while E is false ; and E must be false if only I be 
true, while A is false. In either of these cases A and E are 
false together. A and E, therefore, are only contraries, not 
contradictories; this latter name being reserved for propo- 
sitions between which the opposition is more thorough-going. 

5. This " contradictory opposition " takes place between A 
and 0, and also between E and I. We can say, " If A be true, 
is false ; and if be true, A is false : also, if A be false, O 
is true ; and if be false, A is true." E and I contradict each 
other in the same way. 

To explain this thorough-going contradiction we must par- 
ticularly note that the designation " some," which belongs to 
/ and 0, indicates an indefinite number which may include the 
whole class. It does not mean " some only," or " some, not all," 
but "some at least," "some, perhaps all." Only that un- 
restricted " some " which may prove to be " all," can form the 
contradictory of an universal statement. For, in case there be 
a class of beings called " men," one of three contrary alterna- 
tives must follow concerning any characteristic of them — say, 
wisdom. Either " all men are wise," or " some, not all, are 
wise" (in other words, "some are wise and some are not 
wise"), or "no men are wise." Now the indefinite statement 
designated by 0, that is, " some men — some at least, perhaps 
all — are not. wise" is a general alternative including both 
the second and third of those just given as the contraries of the 
universal affirmative. It may, therefore, be regarded as the 
only alternative of A. But when one or other of two con- 
flicting alternatives must exist, these are the contradictories 
of each other. Hence A and are contradictories. In the 



178 THE MODALIST. [Chap. XIX. 

same way E and I are contradictories. For i" is a general alter- 
native including the first said second of the three mentioned above. 

6. Since the "some" of I and does not preclude univer- 
sality, we cannot argue from i" that A is not true, nor from 
that E is not true. Sometimes, however, as we have seen, 
" some " has a strictly partial, or partitive, meaning. In that 
case the partitive affirmative and the universal affirmative are 
contraries ; and so are the partitive negative and the universal 
negative. For if " only some men are wise " it is not true that 
"all men are wise," and if "only some men are not wise " it is 
not true that "no men are wise." These partitive, or exclu- 
sively partial, propositions, are worthy of notice, yet need not 
be given any formal place in logic. For every such statement 
is compounded from two particular predications of the ordi- 
nary kind, made at once and in modification of each other. 
Should we, in saying, " Some animals are oviparous," so em- 
phasize " some " as to signify " some only," this would be equiv- 
alent to saying, "Some animals are oviparous and some are 
not oviparous " ; and the effect of this double statement would 
be the same as that of I and operating together. 

7. Finally, the opposition of sub-contrariety exists between 
/ and 0. These are styled subcontraries, partly because they 
are subalternates to the contraries A and E, but also because 
they have a peculiar contrariety of their own. For, while we 
infer the falsity of either contrary from the truth of the 
other, but not the converse of this, so we may infer the truth 
of either subcontrary from the falsity of the other, but not 
the converse of this. Contraries cannot both be true, though 
they may be both false ; subcontraries cannot both be false, 
though they may be both true. If it be false that "some men 
are wise," it is true that "no men are wise"; and this justifies 
the subalternate ^some men are not wise." If it be false that 
" some — or any — men are not wise," then " all men are wise" ; 
and this justifies the subalternate "some men are wise." In- 
asmuch, however, as we seldom use a particular conclusion 
when the antecedent warrants an universal assertion, the 
inference of the truth of one subcontrary from the falsity of 
the other occurs but seldom. 



Chap. XIX.] THE OPPOSITION OF PBOPOSITIONS. 179 

8. Comparing the different modes in which pure categorical 
propositions may be opposed to one another, we find the most 
important to be that of contradiction. This yields the follow- 
ing sequences : 

A true, then false ; A false, then true. 
E true, then I false ; E false, then /true. 
I true, then E false ; / false, then E true. 
true, then A false ; false, then A true. 

Next in importance is contrary opposition. This yields : 

A true, then E false ; E true, then A false. 

But there is no sequence, in contrariety, from^l false, or E false. 
Next subordination, or superalternation, yields : 

A true, then I true ; E true, then true. 

But it gives no necessary conclusion from / true, or true. 
Finally, subcontrariety gives : 

/ false, then true ; false, then /true. 

But it yields no necessary sequence from the assertion of I or 
of 0. 

Examining critically all the foregoing modes of sequence it 
appears that the truth of an universal assertion (whether A 
or E) involves either the truth or the falsity of every one of 
the three propositions which may be opposed to it. In like 
manner the falsity of a particular assertion (whether I or 0) 
determines the truth or the falsity of every one of the three 
propositions which may be opposed to it. Therefore to assert 
an universal and to deny a particular are the strongest modes 
of predication. The weakest modes are those asserting the 
falsity of an universal or the truth of a particular ; because 
each of these determines only one out of the three opposed 
judgments. 

9. If now we turn to the mutual opposition of modal cate- 
goricals, we shall find in it an essential correspondence to that 
of pure categoricals, and at the same time, peculiarities arising 
from the fact that it pertains to more abstract and searching 
modes of thought. The universal dogmatic proposition ex- 



180 THE MOBALIST. [Chap. XIX. 

presses necessity, either positive or negative; and the par- 
ticular dogmatic proposition expresses a contingency, either 
positive or negative. In conformity with this we find, in 
modal propositions, contrariety between the necessary and the 
impossible j subalternation between the necessary and the 
possible to be, and between the impossible and the possible 
not to be ; contradiction between the necessary and the pos- 
sible not to be, and between the impossible and the possible 
to be ; and subcontrariety between the possible to be and the 
possible not to be. 

In this statement the terms " necessary " and " impossible " 
signify the necessary to be and the impossible to be, this 
latter being only the necessary not to be, viewed in a peculiar 
way ; just as the necessary to be is the impossible not to be. 

Let us take the propositions, " The tea-plant must — or cer- 
tainly will — grow," " The tea-plant cannot grow," " The tea- 
plant may grow," and "The tea-plant may not grow"; noticing 
that in this last the negative particle does not qualify " may," 
but attaches the idea of non-existence to "grow." These asser- 
tions cannot all be true under the very same antecedent, or 
set of conditions ; yet each must be true provided its own 
proper antecedent exist. For, (1) in cases yielding all the 
needful conditions of soil, climate, cultivation, and so forth, 
the tea-plant must grow ; (2) in cases where any of the need- 
ful conditions is wanting, it cannot grow ; (3) in cases where 
some conditions are known, but others are not known, to 
exist, we say that it may grow ; and (4) in cases where some 
of the conditions are not known to exist, though some are 
known to exist, we say that it may not grow. Let us desig- 
nate these four styles of assertion by the accented letters 
A' E' V and 0'. 

10. A' and E' are contraries. They cannot be true together, 
and they may be false together. With the same antecedent it 
cannot be both necessary and impossible that the tea-plant 
should grow. Moreover, the facts obtainable in the case may 
justify neither of these judgments, but only some form of con- 
tingency. For in all these judgments the antecedent is the 
tea-plant considered as in some set of circumstances or other; 



Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 181 

and in a contingent judgment the antecedent would be the tea- 
plant in the cases marked (3) and (4)} which are, in truth, 
but two aspects of the same case. With this antecedent both 
A' and E' would be false, that is, unwarranted, judgments ; as 
they would be after any antecedent which merely justified 
contingency. If we knew simply that a man was sick, it would 
be a false judgment to say either that he must die or that he 
cannot die. The antecedent only warrants " he may die " and 
" he may not die." For some sick men die and some do not. 
If, indeed, the man is found to have consumption, we may say, 
" He must die " ; or, if he has but a headache, we may say, 
"He certainly will not die"; but in these cases new ante- 
cedents are used. The simple antecedent of " sickness " does 
not make death either necessary or impossible. 

11. A' and /', as also E' and 0', are respectively superalter- 
nate and subalternate. For there is a sense in which whatever 
is necessary is possible to be, and whatever is impossible is 
possible not to be. Whatever must be so, may be so ; whatever 
cannot be so, may be not so. In the former case existence, and 
in the latter non-existence, consists with given surroundings. 
Yet this inference of contingency from necessity, or from 
impossibility, is only partial. For possibility and contingency, 
in the ordinary and proper sense of these terms, involve the 
possibility of the opposite. They are perceived when some of 
the conditions of a thing are known to exist, and some are not 
known to exist. Only the first of these things follows from a 
known necessity ; only the latter from a koown impossibility. 
Contingency, therefore, is said to follow from necessity, only 
because necessity implies the positive part of the foundation of 
contingency ; and it is argued from impossibility only in that 
impossibility implies the negative part of the foundation of it. 
These, however, are the elements which give importance to 
positive and negative contingency respectively. 

The inference of the subalternate particular from the uni- 
versal, in pure categoricals, has this same partial and one-sided 
character. We cannot fully infer "some, perhaps all, are," 
from " all are," nor " some, perhaps all, are not " from " none 
are." The "some " part follows, but the " perhaps" part does 



182 THE MODALIST. [Chap. XIX. 

not. Indeed, as the "perhaps " implies the possibility, or con- 
tingency, of "not all," it really conflicts with the universal 
judgment. 

The inference of subalternation shows only that the par- 
ticular — or the contingent — proposition has been in the right 
direction, not that it has expressed the full and exact truth ; 
and as subordinate to the universal and the necessary, the par- 
ticular and the contingent cannot be taken to mean that the 
superalternate proposition may not be true. They set forth 
only that peculiar particularity and possibility — or partitive- 
ness and contingency — which are not apposed to, but involved 
in, the universal and the necessary. 

12. Again, the modals A' and ' are the contradictories of 
each other, as are also E' and I'. For if it is true that a thing 
must be so, it is false that it may not be so; and if it is true 
that a thing may not be so, it is false that it must be so : also, if 
it is false that a thing must be so, it is true that a thing may 
not be so; and if it is false that a thing may not be so, it is 
true that it must be so. likewise, if it is true that a thing 
cannot be so, it is false that it may be so; and if it is true 
that a thing may be so, it is false that it cannot be so; also, 
if it is false that a thing cannot be so, it is true that it may 
be so; and if it is false that it may be so, it is true that it 
cannot be so. 

13. In these inferences, however, two peculiarities are to be 
observed in the significations of "may not" and "may" — two 
modifications of meaning which are not always, or necessarily, 
attached to these words. 

First, when the falsity of one contradictory follows from 
the truth of the other, " may " denotes an absolute possibility 
to be — a possibility which cannot be displaced by impossibil- 
ity ; so that, with the given antecedent, the thing is certainly 
not impossible : while " may not " signifies an absolute possi- 
bility not to be ; so that — the antecedent remaining without 
addition or alteration — the thing is certainly not necessary. 

Secondly, when the truth of one contradictory is inferred 
from the falsity of the other, the word "may" is not used 
simply, but means "may, perhaps must" (equivalent to "may 



Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 183 

or must"), while "may not" means "niay not, perhaps can- 
not," (equivalent to "may not or cannot"). 

Without these significations of " may " and " may not " the 
inferences of contradiction would not take place. The force 
of these words as thus modified may be inadequately expressed 
by saying that " may " means " certainly may, possibly must," 
while "may not" means "certainly may not, possibly cannot." 
These meanings — it will be noticed — correspond exactly to 
the " some, perhaps all," and the " some, perhaps none " of the 
dogmatic subcontraries. But they belong to a wider and more 
searching range of thought. 



14. In some of the foregoing statements the term contin- 
gency has been used interchangeably with possibility, the rea- 
son being that contingency is based on possibility, and by 
reason of its radical nature, shares in the oppositional relations 
of possibility. As regards subalternation and contradiction the 
possible and the contingent are one ; and, as we have seen, 
each of these modes of opposition may be said to involve a 
specific form of possibility of its own. 

A clearer understanding of these teachings can be had if we 
consider four styles of possibility, in all of which the essential 
conception of the consistency of the existence — or of the non- 
existence — of a thing with given circumstances, is modified by 
some addition. 

First of all, there is that possibility which is perceived as 
accompanying necessity, positive or negative — in other words, as 
accompanying necessity and impossibility. That which neces- 
sarily exists, is recognized as possible to be ; and that which 
necessarily does not exist, is recognized as possible not to be. 
That which must be, may be ; and that which cannot be, may 
not be. The positive form of this possibility may be said to 
be embedded, or infixed, in necessity ; and the negative form to 
be embedded in impossibility. The positive form, therefore, 
cannot co-exist with impossibility, nor the negative with neces- 
sity. Yet a denial of the positive form does not warrant the 
assertion of impossibility, nor a denial of the negative form 



184 THE MOBALIST. [Chap. XIX. 

the assertion of necessity. Each form exists only in its own 
mode of necessity, positive or negative; and neither exists in 
case a given antecedent supports neither necessity nor impossi- 
bility. If death were considered possible only because death 
is necessary, a denial of this embedded possibility would not 
involve the impossibility of death. The case might be one of 
a possibility lying between necessity and impossibility, and 
not embedded in either. 

Therefore this embedded possibility is not that according to 
which the contingent negative contradicts the necessary, and 
the contingent positive the impossible, but merely that accord- 
ing to which the contingent is inferred from the necessary and 
the impossible. For an antecedent of necessity, positive or 
negative, is taken as proof that the existence — or the non- 
existence — of a thing is consistent with a given set of circum- 
stances. We allow that the possibility in such a case is only 
partial and improper. Ordinarily when we say that a thing is 
possible we do not mean that it is possible only to be, but that, 
so far as our knowledge extends, it is possible either to be or 
not to be. So also contingency commonly excludes the asser- 
tion of necessity. But if subalternation be taken as a mode of 
sequence in which the particular follows the universal and the 
contingent the necessary, it must be explained in the foregoing 
way ; and with some such use of terms. 

This mode of opposition, however, may be interpreted to 
mean that the ordinary particular or contingent assertion — 
the " some, perhaps all " or the " may, perhaps must " — is to 
be accepted as partially correct and as made in the right direc- 
tion, provided the apodeictic superalternate be true. We really 
prefer this explanation, though it will not permit us any longer 
to infer the subalternate from the superalternate, but only that 
the subalternate has a certain logical value. 

A second, and an entirely proper, form of possibility is 
recognized, when the very same antecedent which supports a con- 
tingency may, or may not, siipport a necessity, yet is not perceived 
either to do so or not to do so. If one knew only that a lion is 
a quadruped and that a quadruped may and may not be a 
carnivore, he could say, " A lion may be a carnivore," and, " A 



Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 185 

lion may not be a carnivore." In so doing he would use the 
antecedent "lion" correctly, but without knowing the full 
force of it; because, absolutely speaking, the lion is neces- 
sarily a carnivore. Or should one use an antecedent capable 
only of supporting contingency, while he yet knew not of this 
limitation, this would be another species of the kind of infer- 
ence now mentioned. If one knew only that a merchant is a 
man, and that a man may and may not be wise, he could say, 
"A merchant may be wise," and, "A merchant may not be 
wise." But he could not say whether further knowledge might 
not warrant " a merchant must be wise " or " a merchant can- 
not be wise." The contingency thus described may be styled 
" unstable" because further knowledge of the antecedent may 
lead one to displace the contingent by an apodeictic judgment. 
It may also be called " unguarded" because it is not protected, 
as another form of contingency is, against being displaced by 
necessity or impossibility. Evidently no unstable contingency 
can contradict an apodeictic statement ; since the latter may 
prove to be supported by the very same antecedent which is 
employed to support the contingency. 

A third form of possibility or contingency is the stable, or 
guarded. This is recognized when the antecedent is perceived 
to be of a nature to support contingency only; so that no 
further knowledge of the antecedent can justify a judgment in 
necessity or in impossibility. In this case we say that a thing 
is neither necessary nor impossible, but possible to be and 
possible not to be. 

Every judgment in contingency may, on further information, 
be displaced by an apodeictic judgment. This may happen to 
an unstable contingency while the antecedent remains the 
very same ; but it cannot happen in stable contingency so long 
as the antecedent be not essentially modified, or replaced by a 
new antecedent. That ace may appear and may not appear on 
the throw of a die, and that frost may and may not occur on 
New Year's in latitude 40°, are stable, or guarded, possibilities ; 
they cannot, with the antecedents given, become certainties. 

Stable contingency is also perceived when the antecedent has 
been seen to be sometimes accompanied, and sometimes not accom- 



186 THE MODALIST. [Chap. XIX. 

panied, by the consequent. Knowing that man sometimes is 
wise and sometimes not wise, we assert, as a stable contingency, 
" man may be, and may not be, wise." The observed instances 
preclude us from saying that man is necessarily wise, or that 
he is necessarily not wise. It is especially when determined 
in this way that stable contingency may be called guarded. 

This contingency — that is, the assertion of it — denies both 
necessity and impossibility ; because neither necessity nor im- 
possibility can result from one of its antecedents. By it the 
possible to be is opposed to impossibility, and the possible not 
to be to necessity ; and so the positive side of it contradicts 
impossibility, and the negative, necessity; but the force of 
the contradiction comes from that stability which affects both 
sides alike and together. In the same manner necessity and 
impossibility contradict this contingency ; that is, are the con- 
traries of it. 

But a denial of stable contingency does not compel the 
assertion of necessity or of impossibility; it only involves 
that one or other of these is true. The denial of necessity, 
moreover, involves only that the contingency or impossibility 
is true — not that the contingency is true ; and the denial of 
impossibility involves only that the contingency or the neces- 
sity is true, not that the contingency is true. Thus the stable 
contingency, " a quadruped may, and may not, be a carnivore " 
conflicts with both positive and negative necessity ; as each of 
them does with it. But were it false, this would not justify 
us in saying either that a quadruped must be, or that a quad- 
ruped cannot be, a carnivore ; we could only say that one or 
other of these is true ; nor would the falsity of one only of 
these apodeictic statements justify the assertion of the contin- 
gency. Therefore thorough-going contradictory opposition to 
necessity or to impossibility cannot be obtained from stable con- 
tingency. 

There is, however, a fourth style of contingency which does 
yield this opposition. It may be called half-stable, or half- 
guarded, contingency. It is perceived when an antecedent of 
contingency has been seen sometimes to be actually followed 
by a consequent, and has never been seen without the conse- 



Chap. XIX.] THE OPPOSITION OF PBOPOSITIONS. 187 

quent; or when an antecedent lias been seen sometimes to 
occur without the consequent, while it has never been seen 
to be followed by it. In the former case the contingency is 
guarded against impossibility, but may be displaced by neces- 
sity ; in the latter it is guarded against necessity, while it may 
be displaced by impossibility. 

15. A half-stable contingency guarded against impossibility 
may be said to lean, or tend, towards necessity. It is expressed 
exactly, though indirectly, by a particular affirmative asserted 
alone. Thus, " some men are wise " means " man may be wise, 
perhaps must be, and certainly is not incapable of wisdom" A 
half-stable contingency guarded against necessity leans, or 
tends, towards impossibility; and is expressed similarly by 
the particular negative. Thus, " some men are not wise," as 
an isolated statement, means " man may not be wise, perhaps 
cannot be, and certainly is not necessarily wise." 

No terms have been used to designate these two modes of 
half-stable possibility. Let us call that which leans towards 
necessity encouraging possibility, or contingency; and that 
which leans towards impossibility discouraging contingency. 
These somewhat arbitrary terms are the best which suggest 
themselves. 

We are prepared, now, to state what forms of contingent 
assertion are the thorough-going contradictories of necessity 
and of impossibility. Necessity is thoroughly antagonized by 
discouraging contingency, and impossibility by encouraging con- 
tingency. If we assume simply that " some men are wise," we 
can assert the encouraging contingency "man may be wise." 
Then we can say, if it is true that " man may be wise," it is 
false that " man cannot be wise " ; if it is false that " man 
may be wise," it is true that " man cannot be wise " ; if it is 
true that "man cannot be wise," it is false that "man may be 
wise " ; and if it is false that " man cannot be wise," it is true 
that "man may be wise." In short, encouraging contingency 
and impossibility thoroughly contradict each other ; and so do 
discouraging contingency and necessity. 

The main object of the foregoing discussion has been to 
bring out the inner nature and meaning of those particular prop- 



188 THE MOBALIST. [Chap. XIX. 

ositions which are the thorough-going contradictories of universals. 
Evidently they are at heart a peculiar kind of contingent 
modals. Hence, too, it should be noticed that the symbols /' 
and 0', as used to indicate the contingent equivalents of par- 
ticular propositions, relate only to half-stable contingency, and 
not to contingency in general. The prominence thus given to 
half-stable contingency is not unreasonable : dialectically this 
is the strongest mode of contingency; and it is of peculiar 
value when we are seeking the actual, and not merely the 
possible or the probable. 

16. Finally, the relation of subcontrariety exists between 
the propositions just described, that is, between I' and 0', as 
half-stable contingencies. For if either of these be false the 
other is true. Yet, critically speaking, this sequence does not 
take place exactly. The exact sequence is from the falsity of 
I' or of 0' to the truth of the opposite embedded contingency. 
A corresponding inaccuracy appears when we say that the 
falsity of a particular proposition involves the truth of the 
opposed particular. For the falsity of "some, perhaps all, 
are," does not involve the doubtful conclusion that "some, 
perhaps all, are not," but the absolute conclusion that " some, 
as a part of all, are not " ; and the corresponding inference 
from the falsity of "some are not," is that "some, as apart of 
all, are." The falsity of one subcontrary shows that the other 
has been made in the right direction, though it has fallen 
short of the truth; this is all that the logical rule can be 
taken to mean, whether the propositions be pure or modal. 
For the subcontraries are really, not embedded, but half- 
guarded, contingencies. 

These modal subcontraries agree also with the pure subcon- 
traries in that the truth of either does not involve either the 
truth or the falsity of the other. That " some (perhaps all) 
men are wise " does not involve that " some (perhaps all) men 
are not wise," because the first of these statements implies that 
we may find all men to be wise, in which case " some men are 
not wise" would be entirely false. But the two particular 
propositions will be true together, so far, at least, as regards 
their " some are " and " some are not," in case we do not find 



Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 189 

all men to be wise. In like manner, " man may be, perhaps 
must be, wise " does not involve " man may not, perhaps can- 
not, be wise," because, if man should prove to be necessarily 
wise, this would show that the discouraging contingency had 
been falsely asserted. Indeed, in the strictest sense, encourag- 
ing and discouraging contingency conflict with each other. 
Yet, should we find that, though man may be wise, he is not 
necessarily wise, then both the positive and the negative con- 
tingency would be true so far as the "may" and the "may 
not " are concerned. 

17. Probability has not been mentioned in the above dis- 
cussion. The oppositional relations of this mode of sequence 
are essentially those of possibility ; and belong to probability 
as being based on possibility. Probability presupposes some 
form of contingency proper ; and may be divided into unstable, 
stable, and half-stable, according to the style of contingency 
on which it is based. In unstable probability the ratio of the 
chances is determined provisionally and temporarily ; because 
the very same antecedent which yields probability may be 
found to yield certainty. In half-stable probability the ratio 
of the chances is guessed at roughly ; because our knowledge 
extends only to instances favoring one side. Permanent, 
duplicating, or recurrent probability, which is the leading form 
of this mode of assertion, is " stable " ; and as such, while not 
justifying either the subalternation or the thorough-going con- 
tradiction of judgments, conflicts with both necessity and 
impossibility. 

The importance of modal opposition relates to the con- 
tradictions between possibility (including contingency) and 
necessity; it is not connected with the specific nature of 
probability. 



190 THE MODALIST. [Chap. XX. 



CHAPTER XX. 

THE CONVERSION OF PREDICATIONS. 

1. The conversion of dogmatic, or "pure," propositions. 2. Requires 
a substantialized and quantified predicate. Proceeds on the principle of 
Identity. 3. The ordinary conversion of affirmatives. 4. And of the uni- 
versal negative. "Not," as the exclusive particle. 5. Particular negatives 
must be converted by "contraposition," or " infinitation." 6. Conversion 
"per accidens," or "by limitation." Conversion "per differentiam," or 
by "the retained-necessitant." " Simple " conversion. 7. The quanti- 
fication of modals. 8. The universal- necessary and the particular-con- 
tingent. 9. The universal- contingent. 10. The particular- necessary. 
11. Quantity is non-essential to modal thought. The ordinary converse of 
a necessity is a simple contingency ; but sometimes we convert with the 
retained-necessitant. 12. The ordinary converse of an impossibility is an 
impossibility. 13. The conversion of contingency. Always follows " the 
asserted-consequent.' ' 14. Contingent and particular conversion compared. 

1. Conversion, or, more expressly, conversional sequence,, 
takes place whenever from a given proposition another is 
inferred in which the same terms appear but with an exchange 
of places. Like oppositional sequence it is not dependent on 
any reference to a previously perceived similar sequence ; and 
is, therefore, orthologic. The antecedent proposition is called 
the convertend; the consequent proposition, the converse. 
The subject of the convertend furnishes the predicate of the 
converse, and the predicate of the convertend the subject of 
the converse. For example, from " all men are mortal " we 
infer that " some mortals are men." 

Propositions purely factual, or historical, may be converted. 
Because "Mr. Harrison is president elect," we can say "the 
president elect is Mr. Harrison." From " some rogues are on 
that jury " it follows that " some on that jury are rogues." 
Such inferences not only follow the law of Identity (Chap. XV.), 
but are entirely explained by means of it : no study is required 



Chap. XX.] THE CONVERSION OF PREDICATIONS. 191 

to understand them. The conversion now to be discussed per- 
tains to those illative propositions which may be used as prin- 
ciples in reasoning, and especially to categorical predication as 
expressing general hypothetical sequence. Let us consider, 
first, the conversion of pure, or dogmatic, categoricals ; and, 
after that, the conversion of modal predications. 

Before commencing this discussion it should be observed 
that not all propositions are convertible ; only those which 
have been distinguished as inherential statements, or predica- 
tions proper. Presentential propositions cannot be converted, 
because they never set forth a sequence, nor any relation 
between things, but merely the existence or the non-existence 
of the subject. 

2. The conversion of a dogmatic predication takes place 
only after the predicate of the convertend has been both substan- 
tialized and quantified. Substantialization is effected when the 
predicate is changed from the ascriptional form of thought, 
such as adjectives and verbs express, to the substantal form, 
which is expressed by nouns or their equivalents. In this 
way " all horses have four feet " becomes " all horses are 
quadrupeds " ; and, instead of " no horses eat flesh, or are 
carnivorous," we say, "no horses are flesh-eaters, or car- 
nivora." Then, also, the predicate, which is commonly un- 
qualified in the original proposition, must be given that 
quantity, whether universal or particular, which the nature 
of the sequence warrants. We must say — in thought, at 
least, — "all horses are some quadrupeds," and, "no horses 
are any flesh-eaters." After this quantification every ordinary 
affirmative statement asserts that all, or some, of the subject 
class, are identical with some, at least, of the predicate class ; 
and every negative statement asserts that all, or some, of the 
subject class, are different from any — and, of course, from all 
— of the predicate class. Thereupon conversion follows on 
the principle of Identity. Because, so far as verbal thought 
goes, the converse of a thoroughly quantified dogmatic propo- 
sition presents essentially the same truth as the convertend. 

But, as ordinary assertion aims only to characterize the sub- 
ject, and does not quantify the predicate, the subject of the 



192 THE MODALIST. [Chap. XX. 

convertend loses its quantity after it becomes the predicate of 
the converse. "All horses are some quadrupeds/' and "no' 
horses are any carnivores/' become, simply, "some quadrupeds 
are horses/' and "no carnivores are horses." The ordinary 
purposes of predication do not require us to think and say 
"some quadrupeds are all (the) horses" and "no carnivores 
are any horses." 

3. The converse both of the universal affirmative and of the 
particular affirmative proposition, is a particular affirmative j 
because ordinary affirmation only identifies the subject with a 
part of the predicate class. "All men are wise" and "some 
men are wise " alike yield " some wise beings are men." The 
converse of the universal, however, may be said to be a 
stronger assertion than that of the particular. 

Quite in consistency with the foregoing, certain universal 
affirmatives are convertible into universal affirmatives ; because 
they are statements which contain more than the ordinary uni- 
versal affirmative. To indicate this, they have been symbol- 
ized by the vowel U, instead -of A ; and we are told that {/may 
be converted into U. This class of propositions comprises all 
those in which the subject is an exact logical necessitant of the 
predicate. Accordingly, " all spirits are sentient " yields " all 
sentient beings are spirits " ; provided the convertend be under- 
stood to teach that spirits have sentiency as a distinguishing 
attribute, or as a specific property. Definitions, also, belong 
to the class U, because they give the exact analytic equivalent, 
of a thing. If " every moral law is a rule of right action," 
then " every rule of right action is a moral law." 

4. Passing to negative propositions, it is evident that all of 
these, when quantified,, assert that all, or some, of the subject 
class, are not any of the predicate class. In other words, they 
entirely exclude from the predicate class all or some of the 
subject class. On this account the particle "not," properly 
enough, has been called "the exclusive particle" ; though this 
designation does not set forth its essential meaning. 

The principle of Identity requires the converse of the universal 
negative to be an universal negative. Hence "no four-stomached 
animal is carnivorous," yields "no carnivore has four stomachs."' 



Chap. XX.] THE CONVERSION OF PREDICATIONS. 193 

5. The particular negative is commonly said to be incapable 
of conversion ; it is more exact to say that the negative propo- 
sition obtained by converting the particular negative has no 
predicative force. " Some colored men are not negroes," with 
quantified predicate, becomes " some colored men are not any 
negroes." The converse of this, " not any — or no — negroes 
are some colored men," is a true converse, yet useless because 
of the indefinite "some" For while negroes are not some colored 
men, they may be some other colored men. This converse does 
not enable us to say either that negroes are, or that negroes 
are not, colored; it does not characterize the subject either 
positively or negatively ; therefore it fails of the essential end 
of predication. 

But while the particular negative does not directly yield any 
usable converse, its contrapositive does ; and, employing this, 
we convert the particular negatively indirectly. " Some colored 
men are not negroes," by contraposition (Chap. XV.), becomes 
" some colored men are men not negroes," a particular affirm- 
ative ; from which we obtain " some men not negroes are 
colored." 

Not only 0, but A, may be, converted by contraposition. The 
contrapositive of "all horses are quadrupeds," is "no horses 
are animals not quadrupeds " ; from which we obtain the con- 
verse, " no animals not quadrupeds are horses." E also may 
be converted in this way. " No men are perfect," yields " all 
men are beings not perfect," and then "some beings not perfect 
are men." But this converse of E is a weak assertion, and is 
seldom used. The particular affirmative alone cannot be con- 
verted by contraposition ; because its contrapositive is a par- 
ticular negative. The contrapositive of " some men are happy " 
is "some men are not unhappy" ; this has no usable converse. 

In every contraposed proposition the original predicate con- 
ception is displaced by its contradictory, and, because this 
contradictory is generally a negative conception, contrapositive 
conversion has been called " conversion by infinitation ; " that 
is, by the formation of negative conceptions. The original 
conception, however, is occasionally negative, and is then dis- 
placed by a positive conception. In this case the conversion 



194 THE MODALIST. [Chap. XX. 

does not depend on infinitation, but on the reverse process ; 
which might be called re-finitation. 

6. The ordinary conversion of A into I was styled by old 
logicians " conversio per accidens" ; which phrase signifies that, 
in the subject of the converse, the predicate conception of the 
convertend is not used simply, but with reference to some 
" accidental " addition. For, in saying conversely, " some ani- 
mals are men," we do not mean that any animals, simply as 
such, are men, but only that certain animals which have char- 
acteristics not necessarily connected ivith the nature of animals in 
general, are men. The same idea is presented when A is said 
to be converted "by limitation." 

Ordinarily, in this conversion of A " per accidens," or " by 
limitation," the subject of the converse loses its universality ; 
it drops part of its force. The converse " some animals are 
men" means only that "some animals are (at least) some 
men." But occasionally, especially in syllogizing, the subject 
of the convertend, as predicate of the converse, retains its 
universality; so that we regally assert "some animals are all 
the men." This mode of converting an universal or apodeictic 
proposition might be styled conversion " per differentiam," or. 
more exactly, conversion "by the retained-necessitant." For 
the subject of the convertend, as predicate of the converse, 
retains its necessitant value, and its " specific " membership in 
the class designated by the other term. 

The conversion of / into /, and that of E into E, are com- 
monly called "simple conversion," because the converse has 
the same quantity and quality with the convertend. This 
language should not be allowed to conceal the fact that these 
conversions depend upon entirely different laws, so far as their 
quantifications are concerned. I is converted on the same 
principle as A, that is "per accidens," or by limitation; E is 
converted on the principle of negational exclusion. 



Let us now turn from the conversion of pure categorical 
propositions to that of modals. Modal conversion reveals the 



Chap. XX.] THE CONVERSION OF PREDICATIONS. 195 

inner significance of dogmatic conversion; and explains the 
conversion of all illative propositions whatever. 

7. At this point we meet the fact that modal propositions 
often quantify their subjects in the same way that dogmatic 
propositions do ; and are compelled to enquire into the mean- 
ing of this quantification. We sometimes say, not simply 
" man must die ; man cannot reach perfection," but " all men 
must die ; no men can reach perfection " ; sometimes, not 
simply " a professor of religion may be a hypocrite ; a liquor- 
dealer may not be a bad man," but "some professors of 
religion may be hypocrites ; some liquor-dealers may not be 
bad men." In short, necessary statements are occasionally 
given universal quantity, and contingent statements particular 
quantity. 

Not only so; we sometimes "distribute" the subject in 
contingent statements, and employ "undistributed" subjects 
in necessary statements. We say, "all soldiers — or any sol- 
dier — may exhibit bravery; some soldiers must die in battle." 

Let us consider, first, universal statements of necessity ; 
secondly, particular statements of contingency; thirdly, uni- 
versal statements of contingency; and fourthly, particular 
statements of necessity. 

8. The universal necessary proposition differs from a simple 
general statement of necessity only in being more explicit and 
emphatic. "All men must die" means that "man, as such, 
must die." If man, simply as man, is mortal, then all men 
must die. But if man were necessarily mortal only when sub- 
jected to influences from which some of the race are free, we 
could not say that "all men must die," or that, absolutely 
speaking, " man must die." In that case we could only say, 
" some men must die," and, with regard to man as such, " man 
may die." Hence the universality of an apodeictic propo- 
sition shows that the statement is made unreservedly, and 
without mental qualification or limitation. It arises from, and 
is used to indicate, the absolute necessity of the statement. 
Therefore, also, when any proposition is given and accepted as 
a rule of necessary sequence and of demonstrative inference, 
the universality may be dispensed with. 



196 THE MOBALIST. [Chap. XX. 

For a similar reason the particular contingent proposition 
need not be regarded as a necessary logical form. " Some pro- 
fessors of religion may be hypocrites," as a general contingency, 
differs as to strength only from the assertion that "a pro- 
fessor of religion may be a hypocrite." Its meaning may be 
expressed without the "some" if we give the word "may" a 
questioning emphasis. It states that a professor of religion 
may be a hypocrite, but suggests also that the realization of 
this contingency is not to be expected under ordinary circum- 
stances. It is consistent with the proposition that many pro- 
fessors of religion cannot be hypocrites. In short, a particular 
contingent proposition respecting a logical class sets forth 
such a weakened contingency as is suggestive of improbability. 
It should be recognized among the forms of modality. Yet 
the weak contingency which it embodies may be conceived and 
expressed without the quantification ; we can therefore sim- 
plify our discussion — so long, at least, as it relates to mere 
contingency — by dispensing with this quantification. 

9. The universal contingent proposition, as might be ex- 
pected, has a force opposite to that of the particular. It 
expresses a strong contingency ; especially when the universality 
is emphasized. " A professor of religion may be a hypocrite " 
is a contingent assertion applicable to every member of the 
class spoken of considered simply as a member of the class. 
This contingency is strengthened when we say, " All professors 
may be hypocrites." The first assertion would consist with the 
knowledge that some professors are not, and cannot be, hypo- 
crites, though not of course, with such knowledge respecting 
any whose character is in question; the second assertion 
excludes such knowledge altogether. The same thoughts are 
expressed by contrasting " any professor may be a hypocrite " 
and "every professor may be a hypocrite." But should we 
omit the contrast and emphasize "any" there would be no 
difference between these statements. 

In short, there is no difference between an universal contin- 
gency and an unquantified contingency, if the latter be under- 
stood absolutely, or as excluding all knowledge of exceptions. 
The statement, " It may be that every liquor-dealer is a bad 



Chap. XX.] THE CONVERSION OF PREDICATIONS. 19T 

man," would express a strong contingency; for it would imply 
that one could not say that the rule has any exceptions. 

10. Finally, propositions which set forth necessity (or im- 
possibility) concerning an undistributed subject, are really con- 
tingent assertions respecting the subject viewed simply. " Some- 
soldiers (that is, some of the logical class ' soldiers ? ) must die 
in battle " expresses the contingent rule, " a soldier may die 
in battle." 

The contingency thus expressed, however, is affected by two 
additions. First, we are informed that the antecedent of con- 
tingency, " a soldier in battle," is sometimes filled out so as to- 
become an antecedent of necessity. This, also, is the essential 
thought expressed by the dogmatic proposition, "some soldiers 
die in battle." Hence, — as necessity conflicts with impossi- 
bility — we are informed that the contingent rule "a soldier 
may die in battle," cannot be supplanted by the apodeictic 
rule " a soldier cannot die in battle " ; it is guarded against 
impossibility. In like manner, the principle of reasoning that 
" some soldiers cannot — or not all soldiers can — be killed in. 
battle," and which, so far as it is a general contingency, is 
expressed by " a soldier may not be killed in battle," cannot 
be supplanted by " a soldier must be killed in battle " ; it is 
guarded against necessity. This addition, whereby a con- 
tingency is guarded against impossibility, or against necessity, 
— or, in general terms, against a necessity of the opposite — 
is important, and cannot be neglected in the opposition and 
conversion of predications. The quantification employed in 
making the addition instrumentally determines and expresses 
the essential character of the proposition as regards modality. 
In short, the " some" of particular necessary propositions sets- 
forth contingency in precisely the same way as the " some " of 
particular dogmatic propositions ; and, in each case, the verbal 
thought should be distinguished and separated from its mental 
meaning. 

Secondly, the " some " of the particular necessary proposition 
indicates that an appreciable proportion of the class '-soldiers" 
are certain to die in battle, and, in so doing, brings before us, 
indirectly, the essential nature of contingency as distinguished 



198 THE MODALIST. [Chap. XX. 

from possibility in general. For, while contingency admits of 
various degrees, all contingency, even the weakest, is a strong 
possibility, circumscribed and determined by a necessity ; and 
therefore such as justifies expectancy. It is possibility con- 
fined to a sphere in which only a limited number of conse- 
quents are possible. 

As in every battle, or set of battles, some soldiers die while 
the rest survive, and there are thus as many events as there 
are soldiers, it follows that any soldier, taken at random, has 
so many chances to be killed and so many to live through the 
battle or the war. One of the deaths may be his or one of the 
survivals ; and one out of the limited total of events must be 
liis. Therefore the possibility of his being killed or not, is a 
circumscribed, or determined, possibility — a contingency. This 
contingency is further strengthened in case the "some " of the 
proposition respecting the class " soldiers," is conceived to be 
a considerable proportion of the " all." 

If the ratio of the " some " to the " all " were fixed and given, 
a regular judgment of probability would take place. But that 
being unsettled, there is only a contingency, which approaches 
a probability without reaching it ; or, if you please, a contin- 
gency which is an undetermined probability, while it is itself 
a determined possibility. Such is the significance of the par- 
ticular assertion of necessity. 

Yet not all contingency asserts that a certain event neces- 
sarily happens to a number of a logical class, and that any one 
in the class may be of that number. If some appreciable pro- 
portion of the balls in a box were red, there would be a con- 
tingency of corresponding strength that the ball first drawn 
out would be a red one j and were a thousand boxes similarly 
supplied, the contingency would be the same for box after box. 
This contingency would assume that one out of the limited 
number of balls in each box must appear ; but it would not be 
based on any knowledge that red balls have appeared, or that 
red balls must appear, any number of times. Yet this contin- 
gency would be guarded, if we knew that there was nothing 
to prevent any ball from being drawn on any repetition of 
the trial; and it would become a definite probability, if we 



Chap. XX.] THE CONVERSION OF PREDICATIONS. 199 

knew the exact number of balls of each, color. Such contin- 
gency differs from that expressed by the " particular " proposi- 
tion in its origin ; but not in its nature, and as a ground and 
mode of judgment. And this being the case, it is plain that 
particular quantification is not necessarily connected with 
guarded contingency, but only with the origin of a certain 
form of it ; which also it naturally expresses. 

11. The foregoing analysis shows how quantification may 
strengthen and weaken, modify and define, modal assertion, 
while yet quantity is no proper part of modal thought, and 
has only a secondary and ministrant place in the expression of 
modality. The essential meaning of any modal proposition 
dispenses with quantification. 

Such being the case, we proceed to the conversion of modals ; 
beginning with the conversion of apodeictic assertions — that 
is, of propositions setting forth unqualified necessity and im- 
possibility. 

The converse of a necessity is a contingency. For, if a man 
must be a mortal, a mortal may be a man. To speak more 
accurately, it is a contingency guarded against impossibility. 
For if man, as such, must be a mortal, then a mortal, as such, H- 
may be a man, but is certainly not iyicapable of being so. This 
exclusion of impossibility, which results from the necessity 
asserted in the convertend, is often implied when we use the 
word " may " alone ; and the exclusion of necessity may be 
implied in using "may not" alone. Then what "may be " 
cannot, on further information, be found impossible, and what 
" may not be " cannot be found necessary. The word " may " 
sometimes indicates an unstable possibility, in which case there 
is no exclusion of impossibility ; it expresses the converse of 
necessity only when this exclusion is understood. 

Moreover, the contingent converse of a necessity is exclusive 
with reference to its subject. The full statement of it is, not 
that " a mortal may be a man," but that " only a mortal may 
be a man." Commonly this exclusion, being unnecessary to 
the course of one's reasoning, is allowed to drop out of thought. 
But sometimes it is essential; and then it must be retained 
and recognized. 



200 THE MODALIST. [Chap. XX. 



a 



This full conversion of necessity might be distinguished as 
differential conversion." It is expressed dogmatically when 
we say, " some mortals are all men." It is a peculiar case of 
limitative, or contingent, conversion. It might be named con- 
version with " the retained necessitant." 

The contingency produced by the conversion of a necessity 
arises from the circumstance that the consequent of a necessary 
sequence conditions its antecedent : because, whenever we can 
assert that a condition of a first thing exists in a second thing, 
Ave can say that the first thing, so far forth, may be — or is 
possible. As the use of this law depends on the assertion of 
the consequent, it may be called the principle of tlie asserted 
consequent. The common rule is, that we cannot assert the 
antecedent because the consequent is asserted ; this, however, 
means only that the antecedent cannot be asserted absolutely, 
or apodeictically ; it can be asserted contingently. This prin- 
ciple is a part of the general theory of conditions. 

12. The converse of an impossibility is an impossibility. 
"A horse cannot fly" ; therefore "a flying animal cannot be a 
horse." This converse has the same modality as the conver- 
tend ; there is no change either from necessity or from nega- 
tion: hence the conversion is called "simple." The simplicity, 
however, is superficial ; there is really a great change. In the 
convertend we reason from an existing subject to a non-existing 
predicate — from an existing horse to the non-existence of a 
flying animal in the horse. In the converse we no longer con- 
ceive of the original subject as existing, and of the original 
predicate as non-existent; but do just the reverse. We reason 
from the existence of the predicate to the non-existence of the sub- 
ject — from the existing flying animal to the non-existence of 
a horse in it. This is a radical change. 

The law governing this conversion is the principle of the denied 
consequent, that is, the principle which requires us to contradict 
the antecedent, if we contradict the consequent, of a necessary 
sequence. That such is the nature of the conversion will be 
evident, if we remember that the impossible and the necessary 
not to be, are the same. "Man cannot be perfect," means "man 
necessarily is not perfect." If now we contradict the conse- 



Chap. XX.] THE CONVERSION OF PREDICATIONS. 201 

quent, "not perfect/' by asserting "perfect," we must contra- 
dict the antecedent "man/' in other words, man as existing. 
Therefore we say, "a perfect being necessarily is not — or 
cannot be — a man." 

An impossibility is also convertible on the principle of the 
asserted consequent. " a man cannot be perfect " has " man " 
for antecedent, and " not perfect " for consequent. Asserting 
this consequent, we have, "a being not perfect may be a man." 
This converse, because of its contingency and of its negative 
subject, does not compare in value with the other, " a perfect 
being cannot be a man." 

Necessity, also, may be converted on the principle of the 
denied consequent. " A war requires an army " has the con- 
verse, "where there is no army, there can be no war." So, 
since a plain must be extended, what is not extended cannot 
be a plain. This converse is apodeictic and absolute; and, 
notwithstanding its negative subject, is quite useful. It gives 
& test for the existence of any subject whose attributes or 
properties are known : if any of these do not exist, the subject 
cannot exist. It also furnishes the means of reducing a false 
statement of necessity to an absurdity. For if, in any instance 
of an assumed antecedent, its alleged necessary consequent can 
be shown to be wanting, this would lead to the contradiction 
and impossibility, that the antecedent known to exist does not 
exist. 

13. The conversion of contingency, positive and negative, 
presents far more difficulty than that of necessity and impossi- 
bility. The laws of contingent conversion can be simply 
stated ; but the intelligent use of them involves an understand- 
ing of the subtle compounded nature, and of the delicate vari- 
ations, of contingent sequence. Besides, the ambiguity of lan- 
guage adds to the inherent obscurity of this subject. This 
especially attaches to the word "may," which sometimes 
denotes a naked, or bare, possibility, such as excites no ex- 
pectancy ; sometimes a clothed, or invested, possibility, which 
alone deserves the name of a contingency ; and sometimes a 
specific mode of contingency : so that the meaning of this word 
must often be a matter for consideration. 



202 THE MOJDALIST. [Chap. XX= 

The general rule for the conversion of a true contingency is 
that we must follow the pvinciple of the asserted, and not that 
of the denied, consequent. " Man may be wise," of which the 
consequent is wise as existing in man, has the converse, " a wise 
being may be a man " ; while " man may not be wise," of which 
the consequent is wise as non-existent in man, has the converse 
" a being not wise may be a man." 

But should we apply the " denied consequent " to the first 
of these convertends, the result, " one not wise may not be a 
man" — though in a certain sense a correct inference — would 
have no predicative force. It sets forth a possibility which 
not only is unguarded against either necessity or impossibility, 
but is also unsupported by any ground for believing that the 
negative sequence contingently asserted has ever at any time 
been realized, or that it ever will be. A precisely parallel con- 
version would be, " a quadruped may be an elephant," there- 
fore "an animal not an elephant may not be a quadruped'' — 
an inference entirely nugatory, because, for aught that the 
convertend teaches, it may" be true that all animals not ele- 
phants are quadrupeds, or that none of them are quadrupeds ; 
and we are given no reason to suppose that any one of them 
ever has not been, or will not be, a quadruped. 

In like manner, applying "the denied consequent" to the 
convertend " man may not be wise," we have " a wise being 
may not be a man," a possibility wholly unprotected, inde- 
terminate, and without predicative force. Because, for aught 
that is given in the convertend, it may be true that a wise 
being must be a man, or that he cannot be a man, and we have 
no reason to believe that any wise being ever was not, or will 
not be, a man. A parallel conversion to this would be, "a 
quadruped may not be an elephant," therefore, " an elephant 
may not be a quadruped." 

14. The conversion of contingent modals is closely related 
to that of particular dogmatic propositions. These latter, in- 
ternally and essentially, are simply the most common and im- 
portant forms of contingent sequence. They are contingencies 
guarded against the necessity of the opposite. Hence the rules 
for their conversion can be explained by the laws of modal con- 



Chap. XX.] THE CONVERSION OF PREDICATION IS. 203 

version, even while they exhibit an apparent contrast to these 
laws. For contingent propositions, positive and negative, are 
converted according to one principle (the asserted consequent) 
which applies to both alike ; while particular dogmatic propo- 
sitions are converted by two rules. I — the particular affirma- 
tive — is converted by "limitation," and — the particular 
negative — by " contraposition." Thus " some men are wise," 
converted by limitation, yields " some wise beings are men " ; 
and " some men are not wise, " converted by contraposition, 
yields " some beings not wise are men." 

This contrast is a result of that form of thought which neg- 
ative propositions ivith a substantal predicate naturally assume, 
and which is especially observable in the pure, or dogmatic, 
negative. In all such propositions we aim to assert the non- 
existence of cm identity. But, ordinarily, the mind, clinging to 
positive conception, instead of asserting that non-existence 
immediately, first conceives, though without assertion, of the 
identity as existing, and then denies its existence. This mode , 
of conception resembles that according to which negative neces- 
sity becomes impossibility. Contraposition destroys the indi- 
rectness of such assertion by immediately attaching the thought 
of non-existence to the predicate, and then substantializes the 
negative conception thus produced. After this change, the 
predicate, "not wise being," truly sets forth the contingent 
negative consequent ; which the original predicate, " wise 
being," did not. Thereupon the contraposed proposition, as a 
consisting of antecedent and consequent, is converted on the 
same principle as the particular affirmative, that is, "by limi- 
tation"; which is equivalent to "the asserted consequent," as 
applied to guarded contingencies. 



204 THE MODALIST. [Chap. XXL 



CHAPTER XXI. 

CONTINGENCY AND ITS CONVERSION. 

A SUPPLEMENTARY CHAPTER. 

1. Contingency distinguished from possibility. 2. Possibility denned. 
3. Contingency, a circumscribed possibility. 4. Either empirical or mathe- 
matical. 5. Involves an opposite possibility, but not an opposite contin- 
gency. 6. Is either guarded (i.e. half-guarded) or unguarded. When 
double, may be doubly guarded. 7. When combined with a prior sequence, 
produces a contingency unguarded, i.e. unassured, against a necessity of 
the opposite. 8. Unguarded mathematical (or intuitional) contingency. 

9. Embedded contingency, is contingency only in an improper sense. 

10. Possibility is converted only by the asserted- consequent ; and according 
to (a) the law of contained-conditions, and (&) the law of the unascertained- 
necessitant. 11. The converse by the denied- consequent has no force, or 
value. 12. The conversion of contingency. Violently rejects the denied- 
consequent. 13. Is effected by the asserted-consequent. 14. Assumes a 
numerical limitation of the predicate of the convertend. 15. Not ordinarily, 
nor necessarily, double. 16. The converse of an encouraging — or guarded 
affirmative — contingency, is an encouraging contingency with a positive 
subject. 17. That of a discouraging — or guarded negative — contingency 
is an encouraging contingency with a negative subject. 18. These unite in 
the double converse of a double guarded contingency. 19. The conversa 
of unstable contingencies are unstable. 20. The conversion of improper— 
or embedded— contingency follows that of the necessity in which it lies. 
21. A scheme of symbols. 

1. The perplexity which has hitherto obscured the exposi- 
tion of modal assertion and reasoning has arisen principally 
in connection with contingent propositions. The nature of 
apodeictic statements is easily understood. He who would 
cut plain roads through the labyrinth of modality must set 
forth the forms and laws of contingent predication. We have 
already attempted this ; but an additional and somewhat inde- 
pendent discussion will be found useful. 



Chap. XXI.] CONTINGENCY AND ITS CONVERSION. 205 

Contingency, as a ground of inference, is that mode of possi- 
bility which excites expectancy ; it may be distinguished from 
simple possibility by the conditions under which it is produced. 

2. Possibility, in the widest sense, is the consistency of the 
existence of a thing with given surroundings. What is con- 
sistent with given circumstances is not impossible in those 
circumstances. This wide possibility shows that the question 
as to the reality of a thing is not absolutely absurd. 

Ordinary logical possibility, however, is more than mere 
consistency, or non-repugnancy. It is the compatibility, or con- 
gruity, of the existence of a thing, with given circumstances. 
Hence it is suggestive of the question of reality, even, while it 
may suggest no answer to this question. For when we say 
that B is possible because A exists, meaning that the existence 
of A involves the existential compatibility of B with the cir- 
cumstances assumed with A, the question arises, "Does B 
exist ? " 

The compatibility, or congruity, of B with given surround- 
ings, rests on the fact that A, as one of those circumstances, 
contains some, at least, of the necessary conditions of B. A 
broken line composed of three straight lines on a plane renders 
a triangle possible because it contains three conditions of a tri- 
angle. But, in order to a suggestive sequence of possibility, 
the conditions contained in the antecedent must be such as 
specially connect themselves with B, the consequent. If they 
are of a very general character, they will not imply the possi- 
bility of B specifically. It would not be a suggestive sequence 
to say that space renders a line, or a triangle, or a field, or a 
house, possible. Such judgments are metaphysical rather than 
logical. But the specific judgments, " a line may be straight," 
" a triangle may be scalene," " a house may be of four stories," 
might prove suggestive and useful. 

Whenever an antecedent of possibility is perceived to con- 
tain such a combination of conditions as necessitates the conse- 
quent, it becomes an antecedent of necessity, as well as of 
possibility. Ordinarily, however, the antecedent of possibility 
either does not have a necessitant force or is not perceived to 
have it ; so that the question of reality is left undetermined, 



206 THE MODALIST. [Chap. XXL 

and even untouched. For, as already said, possibility per se 
suggests no answer to this question. Its judgments result in 
the harmonious construction of thought, but are only negatively 
helpful towards the ascertainment of truth. 

3. Possibility excites expectancy only when it is strength- 
ened into contingency. For contingency is a ground for believ- 
ing, not simply that a thing is abstractly possible, but that it 
actually may be true. 

This latter mode of sequence is often asserted in an unrea- 
soned way, or, rather, by an intuitive and practical exercise of 
the reason. Perceiving that one certain kind of fact or event 
is occasionally followed by another, we not only associate the 
latter with the former, but regard it as contingently connected 
with the other, and to be looked for, with more or less expecta- 
tion, whenever the other occurs. But when we reflect on such 
a judgment, so as to make it understandingly and place it on 
a foundation, we find that the possibility — the contingency — 
which it asserts, is confined to a sphere in which only a limited 
number of events are possible, and in which one of these events 
must take place. Contingency, therefore, is a circumscribed, or 
determined, possibility. 

The essential nature of contingency may be understood from 
the two following illustrations. Should we know that some 
of a limited number, say of a hundred, balls are red, without 
knowing how many, it would be a contingency to any ball 
taken at random to be red. The fact that the ball is one of 
the hundred is the antecedent of contingency; and it has a. 
hundred possible consequents, of which an undetermined pro- 
portion favor the appearance of a red ball. It would be a 
variation of this illustration if there were an indefinite aggre- 
gation of balls, composed of many equal sets in each of which 
there were some red balls ; in this case also it would be con- 
tingent to a ball taken at random to be red. 

Again, if we knew that some snakes are venomous, without 
knowing what proportion, it would be contingent to any snake, 
taken at random, to be venomous. The antecedent here is 
membership in a class of things which sometimes have a cer- 



Chap. XXI.] CONTINGENCY AND ITS CONVERSION. 207 

tain character — in other words, the possession of that snake 
nature, which sometimes is venomous. 

4. So far as the foregoing judgments assert contingent 
sequence they both arise in the same way : they both make an 
indeterminate use of the tychologic principle — " the ratio of 
the chances." But they differ as to the process by which each 
forms and accepts the conception of favoring chances. That 
snakes are sometimes venomous has been ascertained from 
observation, and is the ground for an homologic inference. 
An indefinite proportion of all snakes hitherto seen having 
been found venomous, this may be asserted concerning snakes 
not yet seen : so we say that some of the whole logical class 
are venomous. This justifies the general judgment "a snake 
may be venomous." The contingency, thus expressed, is per- 
ceived only after a previous perception of actual sequences, 
and, with reference to this, may be named inductive, or empirical, 
contingency. But the contingency that any ball of the hun- 
dred or more may be red, rests on our immediate knowledge 
respecting a set, or an aggregation, of balls, that some of them 
are red, and has no connection with any previous experience. 
It does not assume that, in some previous trials, the ball 
chosen at random has turned out red. 

Contingent judgments of this latter formation are less fre- 
quent than those based on the observation of past sequences, 
yet they illustrate better the essential principle of contingency; 
for they make no addition to it. This form of contingency is 
that assumed by mathematicians, and may be distinguished as 
intuitive, or mathematical. J. S. Mill and the Associationalists 
teach that all contingent judgment is empirical, or based on 
observation of the past ; their doctrine gives no satisfactory 
account of mathematical contingency. 

Such is the nature of contingency, not as a general, but as 
a specific, mode of logical sequence. It lies between possibility 
and probability, and is more determinate than the former, and 
less determinate than the latter. 

5. Two characteristics of contingency are closely connected 
with its nature. In the first place, such sequence is always ac- 
companied with a " possibility of the opposite." The " opposite " 



208 THE MOBALIST. [Chap. XXL 

here means the contradictory of that which is contingently 
asserted. When we judge that the ball selected at random 
may be red, or that the snake met accidentally may be venom- 
ous, it is also felt that the ball may not be red, and that the 
snake may not be venomous. This doubleness arises because 
the antecedent of possibility both assures us that some condi- 
tions of the consequent exist, and leaves us in doubt whether 
or not others do ; it therefore justifies both a positive and a 
negative sequence in possibility. But contingency is double only 
when both sides of the possibility are supported by known facts or 
instances. Consequently we cannot say that contingency is 
always double, but only that it is always accompanied by a 
possibility of the opposite. Knowing that some snakes are 
venomous, but not whether any snakes are not venomous, we 
can assert a negative possibility, but not a negative contingency, 
concerning snakes. This negative possibility accompanies the 
positive contingency, like a shadow. So also a positive possi- 
bility accompanies a negative contingency. These possibilities 
differ from the contingencies which they accompany in that 
they are not grounds of expectancy. Because, for aught we 
know, it may be true that they never have been — or that they 
never can be — realized in any case. 

It may be said that the opposite of the contingency asserted 
is supported by any chances that remain after those favoring 
the assertion have been subtracted from the total number; and 
that, therefore, the opposite of a contingency is also necessarily 
a contingency. This, however, is not so. The denial of the 
opposite of the asserted contingency is supported by the same 
chances which support the original assertion, and is also a 
contingency. But the assertio?i of that opposite is not really 
supported by any chances at all. For, as the remainder above 
mentioned may be either some chances or none, we have no 
right to depend upon any. In short, the opposite of the 
contingency asserted, being wholly unsupported by facts or 
instances, is only a naked possibility. 

6. The second characteristic of contingent sequence is that 
it may be either guarded or unguarded. Naturally and prima- 
rily positive contingency is- guarded against impossibility, but 






Chap. XXL] CONTINGENCY AND ITS CONVERSION. 209 

not against necessity j while negative contingency is guarded 
against necessity, but not against impossibility. Each of these, 
therefore, may be* termed half-guarded, or — more simply — 
guarded, contingency ; and, as we shall see, each of them may 
become unguarded. Knowing simply that some snakes are 
venomous we have the guarded contingency, " a snake may be 
venomous " : knowing simply that some snakes are not venom- 
ous, we have the guarded contingency, "a snake may not be 
venomous." These contingencies may combine in the double 
sequence, "a snake may, and may not, be venomous,'* which 
appeals to both positive and negative instances. This, as 
guarded against both impossibility and necessity, may be 
described as doubly guarded. 

7. Contingency loses its guarded character if it be not * 
immediately based on facts, but inferred from the combination 
of a contingency with a prior sequence. Knowing that "a lion 
is a quadruped," and that "a quadruped may be a carnivore," 
we say, " A lion may be a carnivore." Also knowing that " a lion 
is a quadruped," and that " a quadruped may not be a carni- 
vore," we say, "A lion may not be a carnivore." Further infor- 
mation displaces both of these deduced contingencies by a 
necessity. In like manner the similarly inferred contingencies, 
"an ox may be a carnivore" and "an ox may not be a carni- 
vore," give place to an impossibility. Again, some reptiles 
being snakes and some snakes venomous, we say, "A reptile 
may be venomous " ; and, for like reasons, " A reptile may not 
be venomous." Here are two unguarded contingencies ; addi- 
tional knowledge renders each as guarded as those from which 
it has been inferred. An exception to the rule now explained 
will be noticed hereafter. 

Unguarded contingency may be single or double, according 
as the contingency from which it is deduced is single or double. 
In the above illustrations, if we unite the opposite single asser- 
tions, we can say, "A lion may, and may not, be a carnivore," 
"An ox may, and may not, be a carnivore," and, "A reptile 
may, and may not, be venomous." But it is not so important 
to distinguish between the single and the double mode of 
unguarded contingency as it is to distinguish between that 



210 THE MOBALIST. [Chap. XXI. 

guarded contingency which is double, being both positive and 
negative, and that guarded, or half-guarded, contingency, which 
is single, being either positive or negative. Ordinarily con- 
tingency is single, and guarded only on one side. 

8. Mathematical unguarded contingency may be illustrated 
thus : let there be 100 balls of ivory, all of these being white 5 
100 of wood, some of these being red ; and let all the balls be 
placed in one collection. Then if one knew not that all the 
ivory balls are white, but only that (a) they are all among 
the 200, and that (b) some of the 200 are red, it would be a con- 
tingency to an ivory ball to be red. Or, if he knew only that 
(a) all the ivory balls are among the 200, and that (6) some 
of the 200 are white, it would be contingent to an ivory ball 
to be white. Investigation would displace either of these con- 
tingencies by the certainty that every ivory ball is white. But 
if the ivory balls were some white and some red, and this 
should appear on investigation, then the contingent judgments 
respecting the color of any ivory ball (taken at random) would 
become guarded, and stable. For unguarded contingency may 
be termed unstable ; guarded (or doubly guarded) contingency, 
stable ; and the half -guarded, half-stable. 

9. In addition to the foregoing modes of contingency, we 
must mention that fixed, or embedded, possibility, which may 
sometimes be called contingency ; and which is that compati- 
bility of the existence, or of the non-existence, of a thing with 
given circumstances, which may be inferred from necessity, or 
from impossibility. This mode of sequence is possibility or 
contingency only in an improper sense ; for it excludes the 
possibility of the opposite ; but it has a place in logic. 

Comparing with each other the different modes of contin- 
gency proper, we find that guarded contingency is the most 
developed and complete sequence ; half-guarded contingency is 
the most frequently used in reasonings ; and unguarded contin- 
gency is the purest, but also the weakest and least determinate, 
mode of contingent sequence. 



Chap. XXL] CONTINGENCY AND ITS CONVERSION. 211 

The Conversion of Contingency. 

10. The general rule for the conversion of possibility and 
of contingency is that either may be converted by the asserted- 
consequent, but not by the denied-consequent. To understand this 
rule we must discuss first the conversion of possibility, and then 
that of contingency. 

With respect to possibility let us first show that the asserted- 
consequent yields a logical converse, and then that the denied- 
consequent does not do so. 

The following specific formulas exhibit the conversion of 
possibility by the asserted-consequent : 

(1) If the existence of one thing (A) render possible the 
existence of another thing (B), then will the existence of B 
render possible the existence of A. 

(2) If the existence of A render possible the non-existence 
of B, then will the non-existence of B render possible the exist- 
ence of A. 

(3) If the non-existence of A render possible the existence 
of B, then will the existence of B render possible the non- 
existence of A. And 

(4) If the non-existence of A render possible the non-exist- 
ence of B, then will the non-existence of B render possible the 
non-existence of A. 

The non-existence mentioned in these formulas always relates 
to, and is included in, a case in which something is non-exist- 
ent ; it is not non-existence per se. Non-entity, of itself, is 
never either antecedent or consequent ; but cases occur in 
which the non-existence of one thing makes something else 
possible to be, or possible not to be. Those antecedents which 
assume non-existence, are cases of existence modified by the 
non-existence of some element which might have been present. 
Therefore, for the sake of simplicity, we may disregard the 
difference between positive and negative antecedents, and retain 
only the first two of the foregoing rules ; after which these may 
be combined in the one rule that " if the existence of A render 
possible the existence, or the non-existence, of B, then will the 
existence, or the non-existence, of B render possible the exist- 



212 THE MODALIST. [Chap. XXI. 

ence of A." That is to say, any antecedent of possibility may 
be made the consequent of its own consequent. In other words, 
every sequence in possibility may be converted by "the asserted 
consequent." 

This formula may be justified, first, with reference to affirma- 
tive possibility, and then with reference to negative possibility. 
The principle which gives vitality to affirmative possibility 
may be called " the law of contained conditions " ; and the con- 
version of this mode of possibility by the asserted consequent 
follows upon the fact that the law of contained conditions has 
a reciprocal action. For the antecedent of possibility always 
contains a condition, or conditions, of the consequent ; and the 
consequent, a condition, or conditions, of the antecedent. Let 
A be antecedent of possibility to B, because A involves c, which 
is a condition of B. Then, first, c is a condition of A, as being 
involved in A ; and secondly, c is involved in B, as being a con- 
dition of B. This being so, B, as involving c, which is a condi- 
tion of A, may be antecedent of possibility to A. Take the 
sequence, "man (A) may be wise (B)." Here wisdom is pos- 
sible because man has intellect (c), which is a condition of 
wisdom. But intellect is a condition of "man," as being a 
necessary part of him ; and it is involved in wisdom as being 
a condition of wisdom. Therefore, conversely, " a wise being 
may be a man." A coin may be a piece of silver, and a piece 
of silver a coin, because each of these involves "valuable 
metal." A long walk and a wide plain render each other logi- 
cally possible, because each involves the element of "distance." 

The principle which gives vitality to negative sequences in 
possibility is a corollary, or concomitant, of "the law of 
contained conditions " ; it may be named " the law of the unas- 
certained necessitant " ; and this principle, like that which it 
accompanies, has a reciprocal action. In every assertion of pos- 
sibility proper, while knowing that some conditions of an entity 
exist, we are ignorant whether such and so many exist as con- 
stitute a logical, or necessitating, condition. We may know 
that the antecedent, considered per se, does not contain a logical 
condition (or necessitant), or we may be ignorant whether it 
does or not ; in the one case we assert a settled or stable, in the 



Chap. XXI.] CONTINGENCY AND ITS CONVEBSION. 213 

other, an unstable, possibility of non-existence ; in either case 
we assert the possible non-existence of B, because A {either as 
known, or so far as known) does not contain a necessitant of B. 
But the non-existence of B, though involving the non-existence 
of any necessitant of B, and of any antecedent containing that 
necessitant, is consistent ivith what does not contain the necessi- 
tant. Therefore the non-existence of B is consistent with the 
existence of A : " man may be wise " yields, first, " man may 
not be wise," and then the converse possibility, "a being not 
wise may be a man." Therefore, though there is silver there 
may be no coin, and though there be no coin there may be 
silver. 

Ordinarily A is known not to contain a necessitant of B ; so 
that the contingency, " A is possibly not B — man is possibly 
not wise " is guarded against necessity. In this case the con- 
verse, "Not-.B is possibly A — not-wise is possibly man" is 
guarded against impossibility. But should A be only not 
known to contain a necessitant, the convertend would not be 
guarded against necessity, nor the converse against impossi- 
bility. Knowing that a carnivore may not be a quadruped, 
and that a lion is a carnivore, we may say, " A lion may not 
be a quadruped." Further knowledge will displace this by a 
necessity : and the converse, " a non-quadruped may be a lion " 
will be displaced by impossibility. But commonly the con- 
vertend is understood as guarded, so that the converse, also, is 
guarded. So much for "the asserted-consequent." 

11. We are now prepared to ask whether possible sequence 
can be converted by " the denied-consequent," as well as by 
" the asserted-consequent." This point may be discussed as a 
question respecting the validity of two formulas, if, as before, 
we neglect the distinction between positive and negative ante- 
cedents, and so reduce four formulas to two. These are : 

1. If the existence of A render possible the existence of B y 
then the non-existence of B will render possible the non-exist- 
ence of A. 

2. If the existence of A render possible the non-existence of 
B, then will the existence of B render possible the non-exist- 
ence of A. Expressed categorically, these conversions are, 



214 THE MODALIST. [Chap. XXI. 

(1) A is possibly B; therefore, what is not B is possibly 
not A ; and 

(2) A is possibly not B; therefore, B is possibly not A. 
Coin is possibly silver ; therefore, what is not silver is possibly 
not coin. — Coin is possibly not silver ; therefore, silver is pos- 
sibly not coin. In these proposed inferences, as the method 
of " the denied-consequent " requires, the contradictory of the 
consequent is used for antecedent and the contradictory of the 
antecedent for consequent. 

The conversion of a positive sequence is attempted, in this 
way, on the principle that the absence, or contradiction, of the 
antecedent renders the absence of its consequent possible — that 
is, shows it to be possible. For the absence of the antecedent 
puts us in doubt whether even those conditions of the conse- 
quent respecting which the antecedent would give assurance, 
are present or not ; inasmuch as, if they are, it must be in 
some other antecedent. Beyond question the law of "the 
unascertained necessitant " applies here in a very literal way ; 
and so we say, first, "A is possibly B" ; then, "What is not 
A is possibly not B " ; after which, using " the asserted- 
consequent," as with any negative possibility, we obtain the 
converse, "what is not B is possibly not A." "Coin is possibly 
silver — what is not coin is possibly not silver — what is not 
silver is possibly not coin." 

This sequence is correct ; and yet it is entirely nugatory and 
useless. Though supported by the fact that the denial of an 
antecedent of possibility leaves no ground for conjecturing 
that the consequent exists, so that, until we learn more, we 
can say that, so far as we know, the consequent may not exist ; 
it is open to two objections. The fatal objection is that the 
secondary, or intermediate, convert end, from which the con- 
verse is immediately produced, is without convictional value, 
because it is founded purely on "the unascertained necessitanV ; 
which principle is useless except as a concomitant principle. All 
logical force disappears when we form that secondary conver- 
tend, by using contradictory conceptions. Hence no connection 
of congruity or compatibility is perceivable in the converse, 
between antecedent and consequent. 



Chap. XXL] CONTINGENCY AND ITS CONVERSION. 215 

Then, secondly, while the original convertend may be a guarded 
possibility, the converse is unguarded. We correctly say, "A 
quadruped may be a lion — a non-quadruped may not be a lion 

— a non-lion may not be a quadruped." But, notwithstanding 
all this, it might be true that every " non-lion " is a quadruped. 

The conversion of a negative sequence by "the denied-conse- 
quent " may be attempted as follows. " A is possibly not B. 

— jSTot-J. is possibly B. — B is possibly not A." Coin is pos- 
sibly not silver ; what is not coin is possibly silver ; silver is 
possibly not coin. Here, as before, the operation of " the denied- 
consequent " is equivalent to that of the asserted-consequent 
after contradictory conceptions have been employed. 

This conversion, like that just considered, is without con- 
victional force. In saying, " What is not coin may be silver," 
because " coin may not be silver," we base a sequence simply 
on the removal of an antecedent of possible non-existence; we 
assert a possibility because we have no reason either for or 
against it, except the removal of that antecedent. Such an 
assertion is entirely indeterminate ; and so is the converse of 
it, " silver may not be a coin." Moreover, while the original 
possibility may be — and commonly is — guarded, this converse 
is unguarded. Should we say, " A quadruped may not be a 
lion ; therefore a lion may not be a quadruped " ; this converse 
will be displaced, on further knowledge, by a necessity. 

12. We pass, now, from the conversion of possibility in 
general to that of contingency. By this we mean the inference 
of a converse contingency from a convertend contingency ; for to 
infer a possibility conversely from a contingency, would only 
be a conversion in possibility, and not, distinctively, a convex 
sion in contingency. 

While the conversion of contingency follows the same rule 
as that of possibility in general, it has some noteworthy pecu- 
liarities. In the first place, the method of the denied-consequent 
is more violently rejected by contingency than by possibility. This 
method leads to a formal but useless converse in possibility, 
but produces no converse whatever in contingency. The reason 
for this is that the facts or instances which sustain the original 
contingency, do not support the proposed converse contingency. 



216 THE MODALIST. [Chap. XXI. 

The contingency, " a snake may be venomous/' rests on the fact 
that " some snakes, at least, are venomous." This fact yields 
no support to the converse, that " an animal not venomous may 
not be a snake " ; it is not a fact relating to such animals. So 
also the contingency, "a snake may not be venomous," rests 
on the fact that " some snakes are not venomous " ; and this 
does not support any converse contingency respecting " ven- 
omous " animals. In short, the conversion of contingency by 
the denied-consequent, results only in a useless indeterminate 
possibility. 

13. On the other hand, the asserted-consequent produces a 
true conversion ; because the same facts which support the con- 
vertend, support the converse also. The same instances justify 
the contingency, " a snake may be venomous," and the contin- 
gency, " a venomous animal may be a snake." In like manner, 
the contingencies, "a snake may not be venomous," and "a 
non-venomous animal may be a snake," are supported by the 
same instances. 

Mathematical contingency, equally with the empirical, is 
convertible by the asserted-consequent. Let some balls in a 
collection of one hundred be red. Then it is contingent to any 
ball, selected at random, to be red, and to any red ball to be 
the one so taken. Or, if some of the balls be not red, it is 
contingent to any ball selected at random, not to be red, and 
to any ball not red to be so selected. Convertend and converse 
originate together, and are supported by the very same facts. 

14. But, in this connection, it should be remarked that con- 
verse does not follow convertend so absolutely — so perfectly 
as a matter of course — in contingency as in possibility. A 
converse contingency, unlike a converse possibility, depends 
on a limitation which, ordinarily and naturally, attaches to the 
predicate of the convertend, yet which is not necessarily in- 
herent in it. For the class or set of things, to which the sub- 
ject of the converse refers must be numerically limited in order 
that some indefinite proportion — or ratio of chances — may be 
assumed between the "some" and the "all." Without this 
limitation, at least in our first apprehension of the converse 
contingency, no basis of expectancy could be formed. But the 



Chap. XXI.] CONTINGENCY AND ITS CONVERSION. 217 

class thus numerically limited is the same as that to which 
the predicate of the convertend refers. In converting " a snake 
may be venomous," we assume that the venomous animals 
which are snakes belong to a class "venomous," and constitute 
an appreciable proportion of that class. In the converse of 
the negative contingency a similar ratio is assumed between 
the "non-venomous," which are snakes, and the whole class 
"non-venomous." So, in converting the mathematical contin- 
gencies, the " red balls " and the " balls not red " are thought 
of as belonging to the collection in the box ; and not as being 
any red balls whatever, or any balls not red. 

This numerical limitation somewhat resembles "quantifi- 
cation " of the predicate, but is quite another thing j for it is 
not exclusively related to a logical class. 

15. Another difference between contingency and possibility is 
that the conversion of possibility always admits of a doubleness, 
ivhile this is not the case ivith contingency. Every antecedent of 
possibility proper justifies both a positive and a negative con- 
sequent. Hence every positive sequence in possibility is accom- 
panied by a negative sequence, and every negative, by a positive. 
This being so, the converse of a positive possibility is accom- 
panied by the converse of the negative, and the converse of 
the negative by that of the positive. Therefore "a man may 
be wise," as a possibility, has the double converse, "a wise 
being may be a man," and " a being not wise may be a man." 
And, in the same way, both these conversa may be inferred 
from the negative possibility, " a man may not be wise." But 
the positive contingency, " a man may be wise," justifies only 
its own single converse ; and the negative contingency, " a man 
may not be wise," only its own single converse. Neither of 
these contingencies can claim the converse of the other along 
with its own ; because the facts supporting it justify only one 
converse contingency. 

When a positive and a negative contingency are united so 
as to form a double contingency, the converse of the double 
contingency is also double ; but this is not because each con- 
tingency warrants the converse of the other, but only because 
each is followed by its own. 



218 THE MODALIST. [Chap. XXI. 

16. In addition to the supreme law for the conversion of 
contingency some subordinate rules claim attention. These 
pertain to the different modes of contingency according as it is 
proper or improper, guarded or unguarded. In discussing them 
we need not continue to contrast possibility and contingency ; 
for we must employ principles freely applicable to both. 

The most common modes of contingency are that affirmative 
sequence which is guarded against impossibility, and which 
has been styled "encouraging," and that negative sequence 
which is guarded against necessity, and which we have named 
" discouraging." These correspond with the half -guarded modes 
of possibility, positive and negative ; and are based on these 
possibilities. Both may be styled "guarded" in the sense that 
each is guarded against a necessity of the opposite. 

The converse of an encouraging contingency is an encourag- 
ing contingency with a positive subject. If "a man may be wise," 
then " a wise being may be a man." The same instances sup- 
port both these contingencies, and guard both against impossi- 
bility. The strength of the converse depends on the ratio of 
the men who are wise to the whole class " wise " ; and varies 
with our estimate of that ratio. 

17. The converse of a discouraging contingency is an encour- 
aging contingency with a negative subject. If " a man may not 
be wise," then " a being not wise may be a man." The same 
facts justify both these contingencies. The converse is guarded 
against impossibility ; because, by reason of the law of Contra- 
diction, if any subject— A — be not a given predicate — B, then 
A is something which is no't B. Therefore, on the same basis 
of fact, we say, "A man may not be wise — A man may be a 
being not wise — A being not wise may be a man." This last 
assertion is an encouraging contingency. 

A discouraging contingency does not yield a discouraging 
converse, because this would involve " the denied consequent." 

18: Encouraging and discouraging contingency are the two 
modes of half-stable contingency. Stable, or double-guarded, con- 
tingency is the compound from their conjunction. Accordingly 
the converse of stable contingency is tivo-fold, and includes the con- 
verse of each of the constituent parts. Knowing that some men 



Chap. XXL] CONTINGENCY AND ITS CONVERSION. 219 

are wise and some men not wise, we have the stable contingency, 
" a man may, and may not, be wise," with the double converse, 
" a wise being may be a man, and a being not wise may be a 
man " ; each of these assertions being a half-stable encouraging 
contingency. 

But we cannot say, conversely, " A wise being may, and may 
not, be a man," because the negative part of this converse would 
involve the denied-consequent. 

19. The converse of an unstable contingency is an unstable 
contingency. The original assertion being only mediately and 
contingently supported by facts, this must be the case with 
the inferred proposition also. Knowing simply that "some 
carnivores are quadrupeds, and some quadrupeds lions," we 
say, "A carnivore may be a lion." This is an unstable contin- 
gency ; further information might show that a carnivore cannot 
be a lion, or that it must be a lion. For the same reason the 
converse, " a lion may be a carnivore," is unstable ; and further 
knowledge will show that lions are necessarily carnivorous. 

Again, knowing merely that " all oxen are quadrupeds and 
that some quadrupeds are carnivores," we have the unstable 
contingency, " an ox may be a carnivore," and its converse, " a 
carnivore may be an ox." Further information displaces both 
convertend and converse by an impossibility. 

Once more, knowing only that " some mammals are quadru- 
peds and some quadrupeds are carnivores," we have the con- 
tingency, , " a mammal may be a carnivore," and its converse, 
" a carnivore may be a mammal." Both are unstable ; further 
knowledge renders both stable. For it is neither necessary 
nor impossible that a carnivore should be a mammal, or that 
a mammal should be a carnivore. 

The foregoing contingencies are single. Should we say, 
" An ox may, and may not, be a carnivore," because " a quad- 
ruped may, and may not, be a carnivore," we should assert a 
double unstable contingency ; and its double converse, " a car- 
nivore — as also a non-carnivore — may be an ox," would consist 
of two unstable assertions. 

20. The foregoing laws of conversion are those of contin- 
gency proper in its various modes, and do not control fixed, or 



220 TBE MODALIST. [Chap. XXI. 

embedded, contingency. This lias the peculiarity that it may 
be converted either by the asserted consequent or by the denied 
consequent — by the former because it participates in the nature 
of contingency (though not a true contingency); by the latter 
because it shares in the relations of necessity. The possibility, 
"man may be mortal, because man must die," yields not only 
"a mortal may be a man," but also "what is not a mortal may 
not be a man." For this latter contingency is embedded in 
the converse, "what is not a mortal cannot be a man"; which 
is obtained by the denied consequent from the original under- 
lying necessity. In like manner, the possibility, "man may 
not be perfect, because man cannot be perfect," yields, not 
only "a being not perfect may be a man," but also "a perfect 
being may not be a man." This is embedded in the converse 
of the underlying impossibility. 

Such being the case, it is plain that the converse of a fixed 
contingency by the denied consequent is another fixed contin- 
gency. But this is not the result when the asserted conse- 
quent is used. Then tlie converse of a fixed contingency is 
the same as the ordinary converse of necessity (Chap. XX.). 
More specifically, the converse of a positive fixed contingency 
is an encouraging contingency with a positive subject, while 
that of a negative fixed contingency is an encouraging con- 
tingency with a negative subject. Thus the embedded con- 
tingency, "man may be mortal," yields the encouraging 
contingency, "a mortal may be a man" : and, in like manner, 
"man may not be perfect" yields "an imperfect being may be 
a man." 

21. Some advantage might result if the various modes of 
possibility and contingency were indicated by symbols. In 
particular the student might construct for himself a useful 
scheme of those oppositions and conversions in which possi- 
bility and contingency are concerned. To this end we make 
the following suggestions. Let the small Greek vowels i and 
o indicate the positive and negative modes of unguarded, or 
unstable, possibility ; that being the purest form of possibility 
proper. Let possibility as guarded against impossibility be 
marked by the grave accent, thus, I and 6 ; as guarded against 






Chap. XXL] CONTINGENCY AND ITS CONVERSION. 221 

necessity, by the acute accent, thus, C and 6 ; and as guarded 
against both impossibility and necessity, by the circumflex 
accents, thus, 2 and 5. In possibility proper t and o always 
accompany each other. So, also, in the modes of guarded 
possibility, do t and 6 ; I and 6 ; and t and 8. The two modes 
of embedded possibility might be indicated by the same letters 
•enclosed in parenthesis — (t) and (o) . These do not accom- 
pany each other. 

The different modes of contingency might be symbolized by 
■circumscribing with a circle those proper possibilities on which 
contingencies are based. Thus, © and © may indicate single 
unstable contingencies ; © -f- © a double unstable contingency ; 
© and © are half-guarded contingencies ; © -f © is stable 
contingency. 

But, for the sake of simplicity, let the diphthongs ei and ov 
take the place of the circumscribed vowels. Then a and ov 
and et -f- ov indicate the forms of unstable contingency ; et and 
ov the half-guarded contingencies ; and ei + 6v the guarded ; 
that is, the doubly guarded. 

Every single contingency embraces a corresponding possibility 
and is attended by a possibility of the opposite; but not by a 
contingency of the opposite. Thus et and ov do not necessarily 
accompany each other ; but et embraces t, and is attended by 6, 
and ov embraces d, and is attended by L 

So, in unstable contingency, et involves t and o, but not ov ; 
and ovy o and t, but not et. 

The foregoing discussions show that the logician is com- 
pelled to employ the conception of contingency more specifically 
and definitely in connection with the conversion, than in con- 
nection with the opposition, of predications. We account for 
this, because opposition deals with given propositions, while 
conversion is the formation of a new statement ; and because, 
while contingency and possibility, by reason of their common 
nature, may be used in similar dialectic oppositions, their con- 
versions differ by reason of the specific differences belonging 
to them as modes of sequence. 



222 THE MODALIST. [Chap. XXII. 



CHAPTER XXII. 

SYLLOGISMS. 

1. Syllogisms denned. 2. The syllogism-proper. 3. Relational syllo- 
gisms : (a) immediate, (b) mediate. 4. Homologic syllogisms : (a) para- 
digmatic, (&) principiative, (c) applicative. 5. Hypothetical syllogisms. 
6. The consequent-consequent is the first and supreme law of syllogisms- 
proper. 7. The principle of the separating-consequents. 8. The principle 
of the common-antecedent. 9. The principles of syllogistic reciprocation. 

10. These are less independent in their operation than the other laws. 

11. The three propositions, and the three terms, of the syllogism. 12. To 
analyze a syllogism, begin with the conclusion. 13. The four " figures." 
The order of the propositions. 14. Syllogistic moods. 

1. " A syllogism/' says Aristotle, " is a statement in which, 
certain things being laid down, something else, different from 
the premises, necessarily follows in consequence of the prem- 
ises" ("Topics," I. 1). The "things laid down," or "prem- 
ises," are propositions known, or assumed as true; and the 
" something else " is a proposition, either apodeictic or proble- 
matic, necessarily believed in consequence of the premises; 
but the main teaching of the definition is that syllogistic infer- 
ence arises from more than one premise. This, indeed, is the 
essential meaning of the noun <n;AAoyto-/xos as derived from 
the verb avWoy^eaOai. For a-vWoyt^ecrOaL (VvAAeyeiv) indicates 
the gathering, or collecting, of certain elements from given 
premises, and putting them together, so as to form a conclu- 
sion. Yet the plurality of premises does not involve a plurality 
of antecedents ; the combination of the premises is necessary 
to constitute one antecedent. 

Of late years any formal inference, even though it should 
have only one premise, has been called a syllogism. For 
example, "This is an action; therefore there is an agent, — 
This is an event ; therefore there is a cause, — Air is a sub- 



Chap. XXII.] SYLLOGISMS. 223 

stance ; therefore it occupies space, — All trees spring from 
seeds; therefore these trees have done so," — have been classed 
as immediate syllogisms. Let us now restrict the term to infer- 
ences of more than one premise. 

Moreover, as every such inference, when formally expressed, 
either naturally or necessarily uses two premises, let us mean 
by syllogism the statement of a double-grounded inference. 
All the syllogisms of Aristotle have this character. Nay ; the 
forms and rules of syllogizing given by Aristotle, and which 
chiefly call for study, do not apply to every kind of double- 
grounded inference, but only to one important mode of it; 
which, therefore, may be distinguished as the syllogism proper, 
the syllogism par excellence. In the following discussion we 
shall explain the radical nature of the true Aristotelian syllo- 
gism, after first describing some other forms of double-grounded 
inference. 

2. Syllogisms proper are inferences in which from two general 
illative propositions a third general illative proposition is deduced ; 
improper syllogisms are inferences in which from two propo- 
sitions, one of which at least need not be a general illative 
proposition, a third proposition is deduced. 

Dividing improper syllogisms into three classes, according 
to their formative laws, we shall have, in all, four classes of 
syllogisms. These may be named (1) the relational, (2) the 
homologic, (3) the hypothetical, or translative, and (4) the 
catenate. Syllogizing proper is catenated inference ; because, 
by means of it, we form chains of abstract reasoning. 

3. Eelational syllogisms are scarcely worthy of the name. 
They are orthologic sequences made according to different 
specific laws, and are distinguished from other sequences of 
that class only by the complexity of their antecedents. They 
may be subdivided into the (a) immediate and the (b) medi- 
ate ; though these designations are somewhat ambiguous and 
inadequate. The immediate may be illustrated as follows : 

This is a line ; 

And it is straight ; therefore 

It is the shortest possible between its terminal points. 



224 THE MODALIST. [Chap. XXIL 

These lines are straight ; 

And they are parallel ; therefore 

They will continue parallel, however prolonged. 

A and B are respectively equal to C and D ; 
A is added to B and C to D ; therefore 
The sum A + B, is equal to the sum C + D. 

Although the premises of these syllogisms set forth a complex- 
ity of relations, the consequents, " shortest possible," "continued 
parallelism," and "equality of the sums," do not follow the fact 
that a first thing is related to a third through a second. Not- 
withstanding the complex antecedents, the sequences are as im- 
mediate as that from substance to space, or from event to cause. 
Mediate relational syllogisms — or, rather, syllogisms of medi- 
ate relativity, always argue that a first thing is related to a 
third, because it is related to a second which is related to the 
third. Thus we say, 

The line A is parallel to B ; 

And B is parallel to C ; therefore 

A is parallel to G. 

Things are mediately connected by means of spatial and 
temporal relations, and also as having quantity and number, 
as being causes or effects, and as being similar and diverse, 
identical and different. Hence we reason according to such 
laws as these : 

A contains B ; B contains G ; therefore A contains G. 
A excludes B; B contains O; therefore A excludes C. 
A is before B; Bis before G; therefore A is before G. 
A is contemporaneous with B; B with G\ therefore A is contempo- 
raneous with C. 
A is greater than B; Bis greater than C ; therefore A is greater than G. 
A is equal to B ; B is equal to C ; therefore A is equal to G. 
A is equal to B ; B is less than C ; therefore A is less than C. 
A is part of B ; B is part of G ; therefore A is part of C. 
A is like B ; B is like C ; therefore A is like G. 
A is like B, Bis unlike C ; therefore A is unlike G. 
A is the same as B ; B is the same as C; therefore A is the same as d 
A is the same as B ; B is other than C; therefore A is other than C. 
A is part of B ; Bis part of C ; therefore A is part of C. 
A is like B ; Bis C; therefore A is like G. 



Chap. XXII. ] SYLLOGISMS. 225 

Inferences following such laws as the foregoing are " medi- 
ate," because they assert that A is related to C through B. 
But they are not mediate in the sense that a first thing is 
antecedent to a third, because it is antecedent to a second, 
which is antecedent to the third. They do not set forth any 
second thing which is both consequent and antecedent, but 
only a first thing (in which two . relations combine to form an 
antecedent) and a second thing (in which a third relation is 
inferred). In this light they are immediate inferences. 

Eelational inference, and orthological reasoning in general, 
need little logical direction. Every argumentative step must 
be made carefully in accordance with its proper law ; that is 
all. The construction of equations in Algebra and of diagrams 
in Geometry sometimes require an ingenuity which only nature 
and practice can supply ; but the demonstration which follows 
calls simply for a clear intelligence. The rules and hints of 
logic relate chiefly to those syllogizings which pertain to the 
workings of the material and of the moral universe and to the 
practical business of life. 

4. The homologic syllogism is the explicit statement of any 
inference based on the homologic principle ; for all such infer- 
ence is double-grounded. 

The primary form of it is the paradigmatic — the argument 
from example — in which one individual sequence is inferred 
directly from another. 

This powder is poison ; 

That powder is exactly like this ; therefore 

It also is poison. 

In that circle the ratio of diameter to circumference is 3. 1416 ; 
This circle is precisely like that one ; therefore 
Its diameter is to its circumference as 1 to 3.1416. 

The reasoning thus expressed uses analysis and abstraction, 
but not generalization. Yet when we dwell on the inference 
the abstraction runs into generalization ; so that argument from 
example commonly takes the form of reasoning through a 
generalization. This, however, is not always the case; and 
paradigmatization should be recognized as the essential type 
of all homologic inference. 



226 THE MODALIST. [Chap. XXII. 

Next, there is the principiative syllogism, in which we infer 
the general law from the individual sequence. 

This arsenic powder is poison ; 

But all arsenic powder is like this in its composition ; therefore 

All arsenic powder is poison. 

This circle, by reason of its formation has a fixed ratio between diam- 
eter and circumference ; 
All circles are formed like this ; therefore 
All have that ratio. 

John, Thomas, Peter, et ah, die by reason of their constitution ; 
All men are constituted like John, Thomas, Peter, et ah ; therefore 
All are mortal ; or (more abstractly) man is mortal. 

Sometimes the principiative syllogism is called the inductive ; 
but induction is only the most important species of principia- 
tion (Chap. XVI.). 

Finally, the most advanced form of homologic sequence gives 
the applicative, or, as it might also be named, the singularizing, 
or the individualizing, syllogism. This infers an individual 
truth from a general principle. It is easily constructed. The 
major premise asserts a general sequence ; the minor ascribes 
to some individual subject the character of the antecedent of 
the sequence ; the conclusion declares that the consequent fol- 
lows the individual subject individually. 

Man is mortal ; 

Julius Caesar was a man ; therefore 

He was mortal. 

This inference presents no practical difficulty; but we bespeak 
for it careful analysis. For the applicative syllogism, instead 
of being distinguished from the syllogism proper, has been 
taken as the type and example of it. 

Three things are noticeable in the conclusion, " Caesar was 
mortal." First, our thought is changed from the general to 
the individual, or singular; secondly, our conviction is changed 
from the hypothetical to the actualistic; and thirdly, a new 
subject is combined with the predicate of the major premise, 
" Caesar" taking the place of the original subject "man." The 
first two of these changes are justified by the principle that 



Chap. XXII.] SYLLOGISMS. 227 

what is true in the general (hypothetically) is true in the 
particular (actualistically) — which follows from the homologic 
law as combined with the translative principle ; and the new 
subject is warranted by the principle that what belongs neces- 
sarily to any (substantal) predicate belongs also to any subject 
in which that predicate may inhere. Caesar being a man, any- 
thing belonging to a man, as such, belongs to him. The opera- 
tion of this simple orthologic principle is scarcely observable, 
but must be allowed so as to bring " Caesar " under the homo- 
logic reasoning. It does not assume that Caesar must be a 
man, but only the fact that he is a man. 
Turning now to the syllogism, 

Metals are fusible ; 

Gold is a metal ; therefore 

It is fusible, 

we find that the conclusion (a) makes no change from the 
general to the individual, nor (6) any from the hypothetical 
to the actualistic, and (c) that the premise " gold is a metal " 
does not contribute to the conclusion by asserting a fact, but 
by asserting an hypothetical sequence ; the conclusion also being 
an hypothetical sequence. For any predication that is general 
(and not merely a collective assertion) sets forth an hypotheti- 
cal sequence. Clearly this catenate reasoning differs, both in 
its origin and in its effect, from that inference which applies 
general truths to existing individuals. 

The catenate process may be so conceived as to have a super- 
ficial similarity to the applicative inference ; it may even be 
called the application of a general truth to a general subject. 
Nevertheless, as a mode of inference, it differs radically from 
that application which is individualizing and actualistic ; and 
which is pre-eminently applicative. It does not follow the 
law that what is true in the general is true in the individual 
and actual, but the law that the consequent of a consequent 
must be a consequent of the antecedent also. It is not the 
application of principles to realities so as to produce actual- 
istic conviction, but the combination of one general principle 
with another so as to produce a third. 



228 THE MODALIST. [Chap. XXIL 

5. The inference of the actual from the hypothetical, which is 
a factor in applicative syllogizing, often takes place independ- 
ently, and gives rise to a syllogism of its oivn. This inference 
may be styled translative, because it transfers the action of 
the mind from hypothetical to actualistic conviction ; but the 
formal expression of it is known as "the hypothetical syllogism." 
In this the major premise asserts a sequence hypothetically ;. 
the minor either asserts the antecedent of that sequence as 
actual, or denies the consequent ; then the conclusion either 
asserts the consequent actualistically, or denies the antecedent. 
The different modes of this syllogism have been already dis- 
cussed (Chap. XVIII.). 

This hypothetical syllogism (along with the applicative) is 
distinguished from the syllogism proper by reason of the 
peculiar translative law on which it rests ; and it is contrasted 
with all other syllogisms whatever in that it involves no modi- 
fication of our conceptions, but only changes the kind of con- 
viction, with which *our thought is accompanied. 

6. Syllogisms proper arise when two illative propositions 
are combined so as to produce a third, of which the subject, or 
antecedent, is taken from one of the original propositions, and 
the predicate, or consequent, from the other. Moreover, while 
illative propositions are either singular or general, and may be 
combined either in the singular or in the general, the syllo- 
gisms discussed in logic are those of three general propositions. 
Sometimes, especially in mathematical demonstration, we derive 
one singular sequence from the combination of two others ; yet, 
even then, when we dwell on a demonstration for the purpose 
of understanding and testing it, the argument puts on the form 
of generality, and is expressed in the general. 

The syllogism, 

All metals are fusible ; 
Gold is a metal ; therefore 
Gold is fusible, 

is a regular Aristotelian syllogism. So also is this, 

All well- principled persons are trustworthy ; 
Some slaves are well- principled ; therefore 
Some slaves are trustworthy. 



Chap. XXII.] SYLLOGISMS. 229 

The first of these syllogisms consists of three general neces- 
sary sequences. In the second, the first proposition sets forth . 
a general necessary sequence ; the remaining two express the 
general contingent sequences that a slave may be well-prin- 
cipled, and that he may be trustworthy. The law governing 
these two syllogisms is that ivhat involves a consequent involves 
every consequent of that consequent. This expresses their radi- 
cal nature. On the other hand, the syllogism, 

■ 

All conquerors have strong wills ; 

Napoleon was a conqueror ; therefore 

He had a strong will, 

and the syllogism, 

No conqueror is scrupulous ; 
Napoleon was a conqueror ; therefore 
He was not scrupulous, 

do not follow the law of the consequent-consequent, but are 
essentially homologic and applicative. The difference of syllo- 
gisms proper from these syllogisms appears in connection with 
the second premise. When we say, 

Metals are fusible ; 

Gold is a metal ; therefore 

It is fusible, 



the second premise does not assert gold to be actually existent ; 
nor does it speak of this or that gold; but it asserts, hypo- 
thetically, that if, or whenever, or wherever, there is gold, it is 
a metal — that the nature "gold" involves the nature "metal." 
Then, combining this sequence with that of the first premise, 
we obtain, not an individualized truth, but another general 
sequence, "gold is fusible." This result may be used in an 
applicative syllogism concerning this or that gold; but it is JJ 
quite different from the conclusion of such a syllogism. 

The applicative syllogism derives its life and force from the 
homologic principle ; the syllogism proper does not. General 
illative propositions do, indeed, presuppose principiative infer- 
ence, as the origin of their generalization ; and, in all abstract 
argumentation, we assume that we can reason in the general, 






230 THE MODALIST. [Chap. XXII. 

or that general premises will justify a general conclusion. All 
this rests on the homologic principle. Yet the vital force of 
the Aristotelian syllogism is not homological. We reason in the 
general — that is, with general antecedents and consequents — 
just in the same way that we reason in the individual, or with 
individual antecedents and consequents. The premise, "metals 
are fusible," uses the antecedent " metal " and the consequent 
" fusible," and draws its life from their relation as antecedent 
and consequent; the second premise has "gold" for antece- 
dent, and "metal" for consequent; and, just after the same 
fashion, the syllogism, " metals are fusible ; gold is a metal ; 
therefore gold is fusible," follows the law that the antecedent 
of a consequent is antecedent also to the consequent of that 
consequent. 

This law is a self-evident corollary, or accompaniment, of 
the general law of Antecedent and Consequent; it may be 
briefly named the law of the consequent-consequent. But it is 
not the only principal law of syllogizing proper. There are 
three others, each of which assumes the law of the conse- 
quent-consequent, and is logically dependent on it; and two 
of which, at least, have an independent operation. These 
principles may be named the law of "the separating-consequents," 
the law of " the common-antecedent" and the law of " syllogistic- 
reciprocation" All three originate from conversional additions 
to the law of the consequent-consequent ; but they can operate 
independently, because, after any general mode of inference has 
been discovered, it may be used independently of its origin. 

7. The law of the separating-consequents is that if two antece- 
dents have contradictory consequents, one of the antecedents may be 
denied of the other, provided that the premise ivhich is to give the 
consequent of the conclusion can be converted by " the denied-con- 
sequent." This mode of conversion is necessary in order that 
the antecedent of the converted premise may be denied in the 
conclusion; "the denied-consequent " being the only kind of 
conversion which results in denial. Moreover, as only apodeic- 
tic propositions can be converted in this way (Chap. XXI.), 
the premise to be converted must be apodeictic. For example, we 
say, 



Chap. XXII.] SYLLOGISMS. 231 

No material thing is a free agent ; 
Every spirit is a free agent ; therefore 
No spirit is a material thing. 

This conclusion, being a negative predication, has for its true 
consequent "not a material thing"; it means "a spirit is neces- 
sarily not a material thing " ; and this consequent is originally 
reached by converting the first premise and then combining 
the converse with the second premise, according to the law of 
the consequent-consequent. Thus : 

By " the denied-consequent," the premise 

No material thing is a free agent, 

yields, 

No free agent is a material thing : 

then we have the syllogism (of the consequent-consequent), 

No free agent is a material thing ; 
Every spirit is a free agent ; therefore 
No spirit is a material thing. 

This explains the conclusion obtainable by "the separating- 
consequents." 

When both premises are apodeictic, either may be converted 
by "the denied-consequent " ; therefore the antecedent of either 
may be denied of the antecedent of the other. Thus, con- 
verting 

Every spirit is a free agent, 

we have 

What is not a free agent is not a spirit ; 

then, combining this with the other premise of the original 
syllogism, we have, according to the consequent-consequent, 

What is not a free agent is not a spirit ; 
No material thing is a free agent ; therefore 
No material thing is a spirit. 

In this syllogism the second premise has, for consequent, " not 

a free-agent " ; and this is the antecedent of the other premise. 

If, however, either premise be contingent, only the antece- 



232 THE MOBALIST. [Chap. XXII. 

dent of the apodeictic premise can be denied of the other ante- 
cedent. We can say, 

No vices are praiseworthy ; 

Some habits are praiseworthy ; therefore 

Some habits are not vices. 

But we cannot say, 

No vices are some habits, 

or, rather, it would be nugatory and useless to do so. For this 
conclusion is reached by converting the particular, or contin* 
gent, premise by " the denied-consequent " ; and it partakes of 
the worthless character of that conversion (Chap. XXI.). The 
syllogism producing it would be, 

Some things not praiseworthy are not some habits ; 
No vices are praiseworthy ; therefore 
No vices are some habits. 

The law of the separating-consequents is so named, because the 
mutual contradiction of the consequents necessitates the conclu- 
sion that one of the antecedents is excluded, either absolutely or 
contingently, from existing in the same subject with the other. 

8. The law of the common-antecedent is, that if two conse- 
quents have the same antecedent, either consequent may be asserted 
contingently of the other. The operation of this rule requires 
that one premise only be converted by "the asserted-conse- 
quent." Any sequence may be converted in this way ; there- 
fore the common-antecedent is a less restricted principle of 
syllogizing than " the separating-consequents " ; which requires 
the conversion of an apodeictic proposition. 

Moreover, when we syllogize according to the common-ante- 
cedent, the premise converted does not furnish the consequent, 
but the antecedent, or subject, of the conclusion. If it be 
true that 

Some homicides are laudable ; and 
All homicides are cruel, 

then we can say that 

Some cruel things are laudable. 



Chap. XXII. ] SYLLOGISMS. 233 

This conclusion is the " pure," or dogmatic, expression of the 
half-guarded contingency, " a cruel thing may be laudable." It 
is obtained, according to the law of the consequent-consequent, 
after the conversion of the second premise ; as follows : 

Some homicides are laudable ; 

Some cruel things are all the homicides ; therefore 

Some cruel things are laudable. 

A similar half-guarded contingency follows from the original 
premises, if we convert the first, and say, 

Some laudable things are homicides ; 

All homicides are cruel ; therefore 

Some laudable things are — or a laudable thing may be — cruel. 

In converting a negative premise in any syllogism of the 
common-antecedent, we must remember that the consequent 
of a negative sequence is not expressed by the predicate term 
alone, but by that term along with the negative particle. Hence, 
according to the law of the "common-antecedent," the premises, 

No moral precept is a material thing ; and 
All moral precepts are useful, 

yield both the following conclusions : 

Some useful things are not material ; and 
Some non-material things are useful. 

The first of these conclusions evidently follows, according to 
the consequent-consequent, after the conversion of the affirma- 
tive premise by the " asserted-consequent " ; the second follows, 
just in the same way, after converting the negative premise by 
the "asserted-consequent." For inspection shows that the 
consequent of the negative premise is " not material " ; and, 
converting with this consequent, we say, 

Some things not material are moral precepts ; 
All moral precepts are useful ; therefore 
Some things not material are useful ; 

which is a syllogism of the consequent-consequent. 

9. The third subordinate, or, more simply, the fourth law 
of catenate inference, is that of syllogistic-reciprocation. It 



234 THE M0BAL1ST. [Chap. XXII. 

is essentially double ; one part of it pertains to affirmative, or 
conjunctive, reciprocation, and the other to negative, or dis- 
junctive, reciprocation. 

The law of affirmative reciprocation is that " if the consequent 
of a first sequence be antecedent in a second sequence, then the con- 
y sequent of that second sequence may be made antecedent of contin- 
gency to the antecedent of the first sequenced Here we call that 
premise the first whose consequent-term is the antecedent-term 
of the other premise ; and we call the other premise the second. 
This use of terms will be maintained throughout our discussion 
of the laws of syllogistic-reciprocation. 

Both these laws of reciprocation may be explained as con- 
ditioned on the principle of the consequent-consequent; but 
they differ from the subordinate laws already considered, in 
that their explanation involves the conversion of both premises. 
Take, for example, the affirmative sequences, 

Some virtuous men are necessitarians ; and 
All necessitarians are speculators. 

Converted, both by the asserted-consequent, — the latter with 
the retained necessitant, — and reversing the order of the 
premises, we have, by the consequent-consequent, 

Some speculators are all the necessitarians ; 
Some necessitarians are virtuous men ; therefore 
Some speculators are Virtuous. 

This may illustrate the affirmative law. 

The negative law is not so simple. It is that "if, in two 
consecutive sequences, opposite to each other in quality, the predi- 
cate of the first be the subject of the second, a new negative sequence 
may be formed with the predicate of the second sequence for subject 
and with the subject of the first sequence, for predicate; provided, 
however, the first sequence (whether affirmative or negative) be 
apodeictic, and provided also that the negative sequence be apo- 
deictic (whether it be first or second)." More briefly, the first 
(which is, in this case, the "major") premise is always apo- 
deictic; the second (which is, in this case, the "minor") premise 
must be apodeictic in case it is the negative one — otherwise it 
may be contingent. 



Chap. XXII.] SYLLOGISMS. 235 

The negative premise, whether first or second, must be apodeic- 
tic, because a negative conclusion can be obtained only through 
converting that premise by the denied-consequent ; which prin- 
ciple applies only to apodeictic propositions. The first premise 
must be apodeictic, because that premise, after conversion, is to 
furnish the predicate of the negative conclusion. Were it 
contingent, the conclusion could not have an absolute (or dis- 
tributed) predicate; and would, therefore, be useless; like the 
"simple" converse of a particular, or contingent, negative. 

To illustrate : in the following syllogism, the first (or major) 
premise is the negative one, and therefore a contingent minor 
is admissible. 

No moral motivity is an animal impulse ; 

Some animal impulses are principles of action ; therefore 

Some principles of action are not moral motivities. 

Here "principle of action" becomes, by the asserted-consequent, 
antecedent of contingency to " animal impulse " ; then, by the 
denied-consequent, "animal impulse" becomes antecedent of 
impossibility to "moral motivity"; and so (changing the order 
of premises) we reason, by the consequent-consequent, thus : 

Some principles of action are animal impulses ; 
No animal impulse is a moral motivity ; therefore 
Some principles of action are not moral motivities. 

In the following syllogism, the second (or minor) premise is 
negative, and must, therefore, be apodeictic : 

All ruminants have four stomachs ; 

No four- stomached animal is carnivorous ; therefore 

No carnivores are ruminants. 

Were the second premise here a particular negative, it could 
not be converted by the denied-consequent, so as to assert "not 
four-stomached," the contradictory of the consequent of the 
major premise ; without which assertion there could be no neg- 
ative conclusion. But the consequent of the major (four- 
stomached) being thus denied, its necessitant (ruminant) can 
be denied in the conclusion. 

This last syllogism (like all reciprocative syllogisms) assumes 



286 THE MODALIST. [Chap. XXII. 

the consequent-consequent form when we convert both premises, 
and reverse their order ; thus, 

No carnivores are f our-stomaclied ; 

Some four- stomached are all the ruminants ; therefore 

No carnivores are ruminants. 

It also brings before us another instance in which conversion 
"per differential^" or with "the retained necessitant," is neces- 
sary to a valid conclusion. 

10. While both modes of reciprocative syllogizing may be 
accounted for as an operating of the law of the consequent- 
consequent after two conversions, it must be added that 'prob- 
ably such a process is never carried out in our ordinary and 
spontaneous thinkings. Therefore, also, it is yet more unlikely 
that any mind ever uses either law of syllogistic reciprocation 
— but especially the negative one — independently of its origin, 
or mode of formation. Aristotle seems to have been right 
in recognizing only three normal forms of syllogizing. This 
catenate reciprocation is at best an occasional and accidental — 
not a spontaneous and natural — mode of inference. It has 
the appearance of originating in an effort, which cannot be 
directly carried out, to syllogize according to the consequent- 
consequent. 

This led Sir Wm. Hamilton to say that the fourth " figure " 
is a distorted form of the first. But we judge that reciprocative 
arguments are more frequently completed by the methods of 
the "separating consequents/' and the "common-antecedent," 
than in any other way. Positive syllogisms may be completed 
by the latter method, if we only convert the first (or major) 
premise ; and negative by the former, if we only convert the 
second (or minor) premise. Take, for example, 

All greyhounds are dogs ; 

All dogs are quadrupeds ; therefore 

Some quadrupeds are greyhounds. 

Converting the major, we have, 

Some dogs are greyhounds ; 

All dogs are quadrupeds ; therefore 

Some quadrupeds are greyhounds, 

which is according to the "common-antecedent." 



Chap. XXII. ] SYLLOGISMS. 237 

Take also the negative syllogism, 

All ruminants are four-stomached ; 

No four- stomached animals are carnivores ; therefore 

No carnivores are ruminants. 

Converting the second (or minor) premise,. we have, 

All ruminants are four-stomached ; 

No carnivores have four stomachs ; therefore 

No carnivores are ruminants, 

which is according to the " separating-consequents." 

Sneh, then, are the four fundamental modes of catenate 
inference ; in one or other of which every act of syllogizing 
takes place. We shall soon consider according to what laws 
conclusions are sometimes affirmative, and at other times nega- 
tive; also sometimes universal (or apodeictic), and at other 
times particular (or contingent). Let us now complete our 
general survey of the syllogism by defining its essential parts, 
and their properties. 

11. First, a syllogism consists of three illative propositions, and 
only three. This follows from the very nature and definition of 
catenate inference ; and is manifest in connection with each of 
the four laws of syllogizing. The two propositions, which, in 
combination, constitute the syllogistic antecedent, are called 
" the premises " ; the third proposition, which sets forth the 
consequent of that antecedent, is "the conclusion." One of 
the premises furnishes the subject of the conclusion, and is 
called "the minor premise"; the other furnishes the predicate 
of the conclusion, and is called "the major premise." 

In the next place, every syllogism contains three " terms" or 
" extremes," and only three. Verbally, these terms are the gen- 
eral names, or nouns, or nominal expressions, used as subjects 
or predicates in the propositions ; mentally, they are general 
notions, or conceptions. They are called "terms," or "ex- 
tremes," because a proposition may be symbolized by a line 
with the subject at one end and the predicate at the other. 

Only three terms are admissible, and three are requisite, 
according to the essential law of catenate inference — the law 
of the consequent-consequent. According to this law, the 



238 THE MODALIST. [Chap. XXIL 

consequent of the minor premise (either at first, or after such 
conversion as may be necessary) is also antecedent of the 
major; and then the antecedent of the minor and the conse- 
quent of the major form the conclusion. 

Hence, also, one term is always common to both premises. 
This is known as " the middle term " ; because, in the natural 
order of "the consequent-consequent," it comes between the 
other two terms. Of these one is common to the minor prem- 
ise and conclusion, and is called "the minor term"; the other 
is common to the major premise and conclusion, and is called 
"the major term." The terms which become subject and pred- 
icate of the conclusion are designated "minor " and "major" ; 
because, in constructing the most common syllogism — the 
affirmative syllogism of the consequent-consequent — we gen- 
erally conceive of the major term as having wider "extension," 
or application, than the minor. In saying, 

Men have rights ; 

Slaves are men ; therefore 

Slaves have rights, 

the term " slave," in the premises and in the conclusion, has: 
less extension than " have rights." This mode of conception is 
by no means necessary, and does not belong to every syllogism ;. 
therefore the designations "major" and "minor" are somewhat 
arbitrary. 

12. In analyzing a syllogism one should begin with the con- 
clusion, or the proposition to be proved. The order of enuncia- 
tion does not reveal which premise is major nor which is minor; 
either may be enunciated first. The conclusion also may either 
precede the premises, or follow them, or come between them. 
But, in every case, the predicate of the conclusion is the major 
term, and the subject of the conclusion the minor term ; then 
that proposition which contains the predicate of the conclusion 
(together with the middle term) is the major premise ; and 
that which contains the subject of the conclusion (with the middle 
term) is the minor premise. 

13. Thirdly; the "figure" of a syllogism is its character 
with reference to the place of the middle term in each premise.. 



€hap. XXII.] SYLLOGISMS. 239 

That term may be subject of the major, and predicate of the 
minor; then the syllogism is of the first figure : — it maybe 
predicate of both premises; then the syllogism is of the 
second figure: — it may be subject of both premises ; then the 
syllogism is of the third figure : — or it may be predicate of 
the major, and subject of the minor ; and then the syllogism 
is of the fourth figure. Employing the letters P, S, and M for 
the major, minor, and middle terms, and placing the major 
premise first, the figures are as follows : 





Fig. I. 


Fig. II. 


Fig. III. 


Fig. IV. 


Major premise 


. M-P 


P-M 


M-P 


P-M 


Minor premise 


. S-M 


S-M 


M-S 


M-S 


Conclusion . . . 


. S-P 


S-P 


S-P 


S-P 



All syllogisms of the consequent-consequent necessarily 
assume the first figure ; and are known as syllogisms of that 
figure. In like manner syllogisms of the separating-conse- 
quents necessarily assume the second figure ; those of the 
common-antecedent, the third figure ; and those of syllogistic- 
reciprocation, the fourth. 

The question whether major or minor premise should be enun- 
ciated first, has been greatly discussed. It should be answered 
by saying that no absolute rule can be justified. In the order 
of investigation and inferential discovery, the minor premise 
comes first ; for that premise contains the subject of enquiry 
and assertion. But in argument and controversy, the major 
premise is the more prominent. Such, at least, is the case 
with syllogisms in the first three figures ; which are the only 
figures in which we reason spontaneously ; and which alone 
were recognized by Aristotle. 

The fourth figure belongs to a kind of accidental syllogizing, 
in which we set out, or attempt, to use the first figure, and 
then form a conclusion by the aid of conversion. The order 
of its enunciation is subject to the same influences as that of 
the first figure ; and is the same as it would be, if we could 
complete our reasoning without conversion. Hence, in the 
first three figures, the order of discovery places the minor 
premise first; and the order of argument, the major first; while 



240 THE MODALIST. [Chap. XXII. 

in the fourth figure this rule is reversed. The fourth figure 
uses for its minor premise what would be the major premise 
in the first ; and for its major, what would be the minor. 

Moreover, in formal demonstration, we know what we have 
to prove, and may mention it first, if we like. Therefore, in 
every figure, the conclusion may be stated either before or 
after the premises. Aristotle and the Greek logicians did not 
confine themselves to one order of enunciation. They often 
placed the minor premise first ; and sometimes, the conclusion. 
The scholastics and the moderns have favored what is called 
"the synthetic order" ; in which the major premise precedes the 
minor premise and the conclusion. Although this order (except 
in the fourth figure) does not place the middle term in the 
middle of the process of thought, and is therefore secondary 
and artificial, it presents arguments with clearness and force ; 
wisdom also suggests that it be adopted for the sake of uni- 
formity ; and to avoid confusion. 

14. Finally, the " mood " of a syllogism is its character with 
reference to the quality and quantity of its three propositions. The 
Greek logicians called this the syzygy (<rv£vyta) — the combi- 
nation, or " conjugation " — of a syllogism. Of course each of 
the three propositions may be either affirmative or negative ; 
and at the same time, also, each may be either universal or 
particular. In symbolic language, each may be either A, E, I, 
or 0. The mood of a syllogism is stated by using these sym- 
bols to indicate the character of the three propositions. AAA 
is the mood of a syllogism all whose propositions are universal 
affirmatives. EAE is a mood in which the major premise is 
an universal negative, the minor an universal affirmative, and 
the conclusion an universal negative. IAI is a mood in which 
the major is a particular affirmative, the minor an universal 
affirmative, and the conclusion a particular affirmative. One 
of the principal investigations of logic determines what moods, 
and how many, are valid, in each of the four figures. 

The statement that the mood of a syllogism lies in the qual- 
ity and quantity of its propositions, applies only to syllogisms 
composed of pure, or dogmatic, propositions ; and which, there- 
fore, are styled pure, or dogmatic, syllogisms. But the quan- 



Chap. XXII.] SYLLOGISMS. 241 

tity of a dogmatic statement is only the superficial expression 
of its modality ; universal quantity indicates necessity, partic- 
ular quantity, contingency. Therefore, to define mood by its 
relation to internal and mental assertion (6 eV rrj ipvyrj Aoyos), 
we must say that it is the character of a syllogism with reference 
to the quality and modality of its propositions. 

This conception was that which Aristotle entertained ; and 
which he carried out with laborious fidelity. It has the 
advantage of being applicable to all syllogisms whatever, both 
to those composed exclusively of dogmatic assertions, and to 
those constituted wholly, or in part, of modal predications. 
Moreover, as it is not limited to any specific form of state- 
ment, but pertains to the essential nature of catenate infer- 
ence, it will prepare us to admit, and to understand, certain 
delicate syllogistic conclusions which cannot be expressed 
dogmatically. 



242 THE MODALIST. [Chap. XXIII. 



CHAPTER XXIII. 

SYLLOGISTIC MOODS. 

1. If the mood is valid, the syllogism is valid. 2. Any sequence what- 
ever can be converted by the asserted-consequent. 3. Definitional con- 
version. 4. Only apodeictic propositions admit the denied- consequent or 
the retained-necessitant. 5. In syllogisms a negative proposition must 
sometimes be taken as affirmative. 6. Under the consequent-consequent, 
(a) if either premised sequence be contingent, the conclusion must be 
contingent ; (6) if the second sequence (major premise) be contingent, 
the conclusion will be unguarded. 7. An exception to this last rule. 
8. The valid moods of the first figure : AAA, EAE, All, EIO ; and IAI, 
OAO, III, OIO. 9. Of the second figure: AEE, EAE, AOO, EIO ; and 
AAI, All, All, III. 10. Of the third figure : AAI, All, EAO, EIO, IAI, 
OAO; and III, OIO. 11. Affirmative moods of the fourth figure: AAI, 
IAI; and All, III. 12. Negative moods of the fourth figure : AEE, EAO, 
EIO. 13. Contingent premises are commonly guarded. In all the mood- 
formulce they are assumed to be guarded. For any syllogism with an 
unguarded contingent premise must have an unguarded conclusion, no 
matter what be its figure or mood. 14. The negative moods of the fourth 
figure appeal to the separating-consequents ; and its positive moods, to 
the common-antecedent. 15. The consequent- consequent and the sepa- 
rating-consequents are the dominant laws of catenate syllogizing. 

1. We ascertain the specific forms of correct syllogizing by 
determining what moods are valid in the different figures. For 
to say that a certain mood is valid in any figure, is to say that 
two premises of given quality and modality will produce a 
correct conclusion of given quality and modality. To do this 
with a thorough intelligence, one's thoughts should not be con- 
fined to those dogmatic propositions which set forth the recipro- 
cal inclusions and exclusions of logical classes, or to syllogisms 
constructed from such assertions ; the internal and modal syllo- 
gism should be the subject of our investigations. Pure predi- 
cations excellently set forth the most prominent modes of 
logical sequence, yet they are secondary forms of thinking, 



Chap. XXIII.] SYLLOGISTIC MOODS. 243 

and should ever be accompanied by mental interpretation. 
Every syllogism, however immediately conceived, should be 
regarded as constituted of three general sequences ; and the 
laws of syllogizing should be formulated with reference to 
this essential doctrine. 

2. Therefore, in attempting this formulation, some principles 
respecting illative statements must be borne in mind. 

For example, in converting propositions, we must deal ivith them 
as composed of antecedent and consequent, rather than as com- 
posed of subject, copula, and predicate ; and we must apply the 
laws of "the asserted-consequent," the " denied-consequent," 
and the " retained-necessitant." 

Any sequence whatever may be converted by the asserted-conse- 
quent; and will then have an affirmative contingent proposition 
for its converse. "A horse is (necessarily) a quadruped," 
yields "a quadruped may be a horse"; "a horse may be wild," 
yields " a wild animal may be a horse " ; "a horse has no 
horns," yields "an animal without horns may be a horse " ; "a 
horse may not be sound," yields "an animal not sound may be 
a horse." The converse of an affirmative sequence, is an affirma- 
tive sequence with a positive subject ; the converse of a negative 
sequence, is an affirmative sequence with a negative subject. 

It may be said that this conversion of negatives does not 
proceed directly, but is conditioned on a substantialization of 
the consequent, whereby the convertend really becomes an 
affirmative. "A horse may not be sound," becomes first "a 
horse may be an animal not sound " ; and is then converted in 
the same way as an affirmative. This is true ; but this does 
not show that negatives are not convertible by the asserted- 
consequent ; it shows how they are converted by that method. 

3. One exception must be noted to the rule that the asserted- 
consequent produces a contingent converse. Wlien the ante- 
cedent is an exact necessitant of the consequent, an apodeictic 
converse may be asserted. If the elephant is the largest of 
quadrupeds, the largest of quadrupeds is the elephant. Defi- 
nitions and certain mathematical inferences may be dealt with 
in this way (Chap. XX.). 

4. Conversion by the denied-consequent occurs most fre- 



244 THE MOBALIST. [Chap. XXIII. 

quently with the universal negative ; but may be used ivith any 
apodeictic proposition, whether affirmative or negative. "No men 
are perfect/' which means "a man cannot be — or is necessarily 
not — a perfect being," yields "no perfect beings are men/' or 
"a perfect being is necessarily not a man." Here "perfect/' 
the antecedent of the converse, is contradictory of "not per- '■ 
feet/' the consequent of the convertend. In the same way, 
" all men are fallible/' yields " no infallible beings are men/' 
"infallible" being the contradictory of "fallible." This mode 
of conversion always produces an apodeictic negative ; it asserts 
that the antecedent cannot exist when its necessary consequent 
is denied (Chap. XV.). 

Contingent propositions reject conversion by the denied- 
consequent (Chap. XXI.). 

The retained-necessitant is a specific mode which the asserted- 
consequent may assume in the case of apodeictic propositions. 
It produces an affirmative contingent sequence, but has the 
peculiarity that the consequent of the converse retains the 
same absoluteness of application which it had as the antece- 
dent of the convertend. Ordinarily, "all men are mortals," 
yields "some mortals are men," that is, "a man may be a 
mortal"; instead of this, with the retained-necessitant, we say, 
" Some mortals are all the men," or " only mortals are men," 
or " mortals include all the men," or " only a mortal can be a 
man." This conversion being founded on the fact that "mortal" 
is a necessary, not an accidental, ascript of man, it may be styled 
conversion "per differ entiam" ; provided the word "differentia" 
be taken to signify any necessary characteristic. 

Negative necessity is sometimes converted with the retained- 
necessitant; though not so frequently as positive necessity. 
The result of such conversion, in conformity with the general 
operation of the asserted-consequent, is an affirmative contin- 
gency with a negative antecedent. "No men are perfect," 
yields "only imperfect beings are men," or "only an imperfect 
being can be a man," or "an imperfect being, differentially, 
may be a man." 

* That retained absoluteness of conception, which sometimes 
appears in the predicate after the conversion of necessities by 



Chap. XXIII.] SYLLOGISTIC MOODS. 245 

the asserted-consequent, is always retained after conversion by 
the denied-consequent. This latter principle allows no option 
between two styles, or degrees, of conversion. The antecedent 
of the original proposition must be absolutely rejected ; else 
there would be no usable converse. After "no man is per- 
fect " is converted into " no perfect being is a man," the predi- 
cate "man" retains that absolute force with which, in the con- 
vertend, it renders "perfect" impossible. The impossibilitant, 
the necessitant of negation, is retained. 

5. With respect to the combination of propositions as affirma- 
tive and negative, the following rule provides for simplicity of 
statement ; viz., a negative sequence is to be classed with 
affirmatives, whenever it must assume a positive form before 
being connected with the other sequences of a syllogism. For 
example, should we say, 

Wood is not metallic ; 

What is not metallic cannot be used as coin ; therefore 

Wood cannot be used as coin, 

the minor premise, "wood is not metallic," is negative, yet, 
before combining it with the major, we give it an affirmative 
form by mentally substantializing its consequent, and saying, 
"Wood is a thing not metallic." This change is necessary 
in order that the consequent of the minor may become the 
antecedent of the major. In such cases we say that the minor 
premise must be affirmative ; though this is not literally true. 
The exact statement is that it must be affirmative, or, if it is 
negative, that it must be given an affirmative form ; so that its 
consequent may agree with the antecedent of the major. For 
an antecedent conception, even though essentially negative, 
always assumes a positive form. 

The above rule, respecting negative sequences, qualifies and 
interprets the common teaching that affirmative conclusions 
require both premises to be affirmative ; and that negative con- 
clusions require one premise to be affirmative and the other 
negative. Should we say, 

What is not truly valuable is not sought by the wise ; 
The applause of the world is not truly valuable ; therefore 
It is not sought by the wise, 



246 THE MODALIST. [Chap. XXIII. 

we have a negative consequent from two negative premises. 
And should we say, 

What is not compounded is an element ; 
Hydrogen is not compounded ; therefore 
It is an element, 

we have an affirmative conclusion with one of the premises 
negative. But in each of these syllogisms the minor premise 
must be classed with affirmatives. 

6. With respect to the combination of premises as necessary 
and contingent, the following principles should be remembered. 
They apply directly only to syllogisms of the consequent-con- 
sequent, but indirectly to all syllogisms. 

First, when both premises are apodeictic, the conclusion is 
apodeictic ; but if either be contingent, the conclusion must be 
contingent. Moreover, as certainty may be indicated by unity, 
contingency by the ratio of the chances, and the likelihood of 
a compound sequence by the product of the probabilities of its 
parts (Chap. XIX.), a syllogism with one contingent premise 
has a conclusion of the same degree of contingency with that 
premise ; while, if both premises of a syllogism be contingent, 
the conclusion is weaker than either premise. In the argu- 
ment, " Eobbery may lead to murder ; and murder, to hanging 
(or death by electricity) ; therefore robbery may lead to hang- 
ing," the contingency of the conclusion would be equal to the 
product of the fractions representing the separate probabilities 
of the premises ; if those fractions could be ascertained. 

Secondly, the style of the contingency of a conclusion as 
guarded or unguarded — which is a matter of more consequence 
than the degree of the contingency — may be determined by a 
rule in which the minor premise, according to the natural order, 
is conceived of as the first, and the major as the second. This 
rule, of course, applies only to cases in which one of the prem- 
ises, at least, is contingent. It is that if the second sequence be 
apodeictic, the conclusion will have the same style of contingency 
as the first, but if the second sequence be contingent, the conclusion 
will be an unguarded contingency. In other words, if the major 
premise be apodeictic, the conclusion will have the same con- 
tingency, whether guarded or unguarded, as the minor premise, 



Chap. XXIIL] SYLLOGISTIC MOODS. 247 

but if the major be contingent, the conclusion will be an un- 
guarded contingency, no matter what may be the character of 
the minor. For instance, the syllogism, 

A carnivore may be a lion (minor) ; 

A lion is a quadruped (major) ; therefore 

A carnivore may be a quadruped, 

has a conclusion guarded against impossibility; because the 
minor is so guarded, and the major is apodeictic. But should 
we say, 

A lion is a carnivore (minor) ; 

A carnivore may be a bird (major) ; therefore 

A lion may be a bird. 

the conclusion, though a correct conjectural judgment, would 
be unguarded, the major premise not being apodeictic. 

The reason on account of which, in order to a guarded con- 
clusion, the consequent of the prior sequence must be an ante* 
cedent of necessity in the second sequence, is that otherwise 
the antecedent given in the prior sequence might be found to 
be wholly excluded from participation in the second sequence. 
Let A be necessarily, or contingently, B ; and B contingently 
C. Both these things may be true, while yet in every case in 
which A is B, A is not, and cannot be, a B which is a C. 
Therefore a guarded contingency follows only when the minor 
premise sets forth a guarded contingency, and the major is 
apodeictic. 

7. An exception to this requirement of an apodeictic major 
occurs whenever the minor premise has an absolute, or necessitant, 
predicate. This happens not only in exact, or reciprocative, 
necessitations, but also in other cases, such as exist after con- 
version with the retained-necessitant. For example, should 

we say, 

Some books are novels (minor) ; 

Some novels are morally injurious (major); therefore 

Some books are morally injurious, 

the conclusion would be guarded, because all novels are books. 
An abstract statement of this argument would be, 

A is differentially B ; 

B is contingently C ; therefore 

A is contingently C. 



248 THE MODALIST. [Chap. XXIII. 

Here the contingency of the conclusion must be guarded if 
that of the major is ; because, every B being an A, A must 
certainly participate in the contingent relations of B. 

8. We are now prepared to say what moods — or combina- 
tions of propositions — are valid in the first figure ; or, more 
explicitly, in syllogisms of the consequent-consequent. We 
shall speak first of quality ; and then of modality. 

As regards quality, (a) the conclusion of a syllogism in the 
first figure must agree with the major premise; for it always 
asserts the consequent of the major, whether affirmative or 
negative, as following the antecedent of the minor, (b) The 
minor premise must always be affirmative. But this means only 
that if the minor happen to be negative, it must be given a 
positive form, (c) Finally, since the major premise may set 
forth any general sequence, that premise may be either affirma- 
tive or negative. 

With respect to modality, the principle of the consequent- 
consequent allows any combination of premises as apodeictic 
and contingent, with the following restrictions, (d) If both 
premises be apodeictic, the conclusion is apodeictic. (e) If either 
or both be contingent, the conclusion is contingent. But (/) in 
order to infer a guarded contingency, the major premise must be 
apodeictic. 

In the following syllogism, the major premise being contin- 
gent, the conclusion is unguarded : 

One who steals may be caught (minor) ; 

One who is caught may be punished (major) ; therefore 

One who steals may be punished. 

In this syllogism, were the major premise negative, the conclu- 
sion would also be negative ; and would assert " may not be 
punished." 

Such reasonings cannot be expressed dogmatically. We 
cannot say, 

Some who steal are caught ; 

Some who are caught are punished ; therefore 

Some thieves are punished, 



Chap. XXIII.] SYLLOGISTIC MOODS. 249 

because it may be that none of the caught ones who have 
stolen are among the caught ones who are punished. Such 
arguments are declared invalid by those who recognize only 
pure syllogisms. They are not invalid. They are correct con- 
jectural inferences ; and are often used respecting matters of 
probability. 

Admitting them, the major premise may be either A, E, I, 
or ; while the minor (being affirmative) must be either A or 
I. Combining major and minor accordingly, and adding the 
required conclusions, we have the following mood-formulas ; in 
which, according to the common practice, the major premise is 
indicated first, the minor next, and the conclusion last : 

AAA, EAE, All, EIO, and 
IAI, OAO, III, OIO. 

The first four of these, having apodeictic majors, can produce 
guarded conclusions, and can be stated dogmatically : the 
remaining four produce unguarded contingent conclusions ; 
such as that respecting the punishment of the thief. 

An unguarded conclusion is insufficient for the refutation of 
an apodeictic statement. An unguarded is not the contra- 
dictory of A; nor an unguarded I of E. In this sense the 
arguments producing these conclusions are inconclusive. But 
this does not justify the rejection of the unguarded moods ;■ it 
only limits their use to conjectural reasonings. 

9. The controlling law of the second figure is that of the 
separating-consequents. This finds two antecedents which have 
contradictory consequents, and then denies one antecedent of the 
other. Hence, as to quality, (a) one premise must be affirmative 
and the other negative; and (b) the conclusion must be negative. 
But this last means only that the immediate form of the con- 
clusion must be negative. If the antecedent of the major be 
essentially a negative conception, the conclusion, as asserting 
the contradictory of that, is essentially affirmative. In the 
.syllogism, 

No unthinking entity is a free agent (major) ; 
All spirits are free agents (minor) ; therefore 
No spirit is an unthinking entity, 



250 THE MODALIST. [Chap. XXIII. 

the conclusion really signifies 

Every spirit is a thinking entity. 

In short, this rule requiring a negative conclusion is similar 
to that requiring an affirmative minor in the first figure. 

With respect to modality, (c) the major premise must be 
apodeictic. Were it not so, its antecedent could not be wholly 
rejected as the predicate of the conclusion; without which 
rejection there could be no true negation. To say, 

An animal may be a carnivore ; 

A horse is not a carnivore ; therefore 

A horse may not be an animal, 

shows only that a horse may not be some kind of animal — 
not that it may not be an animal. So, 

An animal may not be a carnivore ; 
A lion is a carnivore ; therefore 
A lion may not be an animal, 

gives the same sort of useless conclusion. Then (d) the minor 
premise, as simply furnishing subject and mode of sequence 
for the conclusion, may be either apodeictic or contingent. Finally, 
(e) the conclusion agrees in modality with the minor. For the 
antecedent of the minor supports the contradiction in the con- 
clusion exactly with the force with which it supports its own 
contradicting consequent. 

These rules (a, b, c, d, e) require the major to be either A or 
E ; and allow the minor to be either A, E, I, or 0, provided it 
differs in quality from the major. Hence, syllogisms of the 
separating-consequents have only the following four valid 
moods: AEE, EAE, A 00, EIO. 

But while this is true, it is not absolutely correct to say 
that no other moods than these are admissible in the second 
figure. These are the only negative moods ; in addition to 
these, certain weak affirmative moods, with the middle term 
predicate in both premises, may be justified by a principle of 
their own. For if two antecedents have a common positive conse- 
quent, either may be affirmed of the other, though with an unguarded 
contingency. The strongest conclusion obtainable in this way 



Chap. XXIIL] SYLLOGISTIC MOODS. 251 

from ordinary sequences follows from two apodeictic premises. 
We may say, 

Horses are animals (major) ; 

Quadrupeds are animals (minor); therefore 

A quadruped may be a horse ; 

that is, any quadruped of whose specific character we are igno- 
rant, may be a horse. Notwithstanding the apodeictic premises, 
this conclusion is an unguarded contingency, because it depends 
on that conversion of the major, which leads to the following 
syllogism of the consequent-consequent : 

Some animals are horses ; 

All quadrupeds are animals ; therefore 

A quadruped may be a horse. 

The argument, therefore, is equivalent to one in the first figure 
with a contingent major ; in which, as we have seen, the con- 
clusion is unguarded. 

In these syllogisms of the common-consequent, the premises 
must be affirmative ; because nothing could be inferred if the 
common-consequent were negative. That neither a horse nor 
a quadruped is a stone, does not warrant even a conjecture that 
the one is, or is not, the other. But very weak conclusions 
follow with one premise, or both, contingent. Accordingly we 
have the following affirmative moods : AAI, All, IAI, III. 

Propositions with a common-consequent are easily converti- 
ble into propositions with a common-antecedent ; and the contin- 
gent connection of things is more naturally and fully inferable 
in connection with a common-antecedent than in connection 
with a common-consequent. Therefore the affirmative moods 
of the second figure may be safely neglected, not as incorrect, 
nor even as abnormal, but as weak and needless. 

10. The third figure is governed exclusively by the law of 
the common-antecedent. Hence the moods of this figure may 
be determined, if we remember how the common-antecedent is 
essentially the consequent-consequent, as operating in connection 
ivith a conversion of the minor. For this premise must be con- 
verted by the asserted-consequent, in order that, after conver- 



252 THE MOBALIST. [Chap. XXIII. 

sion, it may have a consequent identical with the antecedent 
of the major. Taking the syllogism, 

All homicides are cruel ; 

Some homicides are laudable ; therefore 

Some laudable things are cruel ; 

and converting the minor, we have, 

All homicides are cruel ; 

Some laudable things are homicides ; therefore 

Some laudable things are cruel ; 

which syllogism of the consequent-consequent arises from 
that conversion by the asserted-consequent ; and could not be 
obtained otherwise. 

Now, no negative premise can be converted by the asserted- 
consequent, unless it be first given an affirmative form. Hence 
one rule of the third figure is that (b) the minor premise must 
be affirmative ; by which we mean only that, if that premise 
happen to be negative, it must be given an affirmative form. 
In the syllogism, 

All moral precepts are useful ; 

No moral precepts are material ; therefore 

Some things not material are useful, 

the minor premise is negative, but must be classed with affirm- 
atives ; because the conclusion depends on its affirmative con- 
verse, that 

Some non-material things are moral precepts. 

After the conversion of the minor, the conclusion adopts 
and asserts the consequent of the major ; hence (c) the conclu- 
sion agrees in quality with the major ; while, as in syllogisms of 
the consequent-consequent, (a) the major may be either affirma- 
tive or negative. 

Modality, in the third figure, is determined as follows:. 
First, while (d)the premises maybe either apodeictic or contin- 
gent, (e) the conclusion is always contingent. Even in the case 
of both premises being apodeictic, the conversion of the minor 
by the asserted-consequent renders that premise contingent; 



Chap. XXIII. ] SYLLOGISTIC MOODS. 253 

and thus causes a contingent conclusion. Secondly, (/) in 
order that a guarded contingency may be inferred, either the major 
premise must be apodeictic, as in the first figure, or, should the 
major be contingent, the minor must be apodeictic. When the 
major is apodeictic, its antecedent, after the conversion of 
the minor, binds the premises together, so as not to allow an 
unguarded conclusion; and when the minor is apodeictic, its 
antecedent performs the same part, after the conversion of that 
premise with the retained-necessitant. The former case does 
not differ materially from that of the first figure ; the latter 
may be illustrated as follows : 

Some homicides are laudable ; 
All homicides are cruel ; therefore 
Some cruel things are laudable. 

Here the conclusion, as guarded, depends on the differential, 
converse of the minor — " some cruel things are all the homi- 
cides/' For, this being granted, it is plain that those cruel 
things which are " some of the homicides " must be laudable ; in 
other words, that it is not an impossibility, but an absolute pos- 
sibility, a guarded contingency, that a cruel thing should be 
laudable. This use of the retained-necessitant is not called for 
in syllogisms of the consequent-consequent, but often occurs 
in connection with the conversions of the subordinate figures. 

Recapitulating the foregoing rules (in a proper order), we say 
that, as to quality, (a) the major may be either affirmative or 
negative, (b) the minor must be affirmative, and (c) the con- 
clusion must agree with the major. As to modality, (d) each 
premise may be either apodeictic or contingent, (e) the con- 
clusion must be contingent, and, (/) to produce a guarded 
conclusion, either the major or the minor must be apodeictic. 

Combining these rules, we find that the major premise may be 
either A, E, I, or ; the minor may be A or J; but in case the 
major is I or 0, the minor must be A ; and the conclusion must 
be either I or 0. Accordingly, in the third figure, the valid 
moods with guarded conclusions are AAI, All, EAO, EIO, 
IAIj OAO. But we must recognize also syllogisms with both 
premises contingent, and whose conclusions, therefore, are un- 



254 THE MOBALIST. [Chap. XXIIL 

guarded ; hence, neglecting the last rule, we form the moods 
III and OIO. The syllogism, 

Some men are intelligent ; 

Some men are unprincipled ; therefore 

Some unprincipled persons may be intelligent, 

is in the mood III. 

11. We pass to the fourth figure, with its two laws of con- 
junctive, and of disjunctive, reciprocation. The former of these 
asserts that if P be the antecedent of M, and M of S, then S is 
antecedent of contingency to P. This calls for a syllogism in 
which the same term, M, is both consequent of the major and 
antecedent of the minor. But an antecedent is always a posi- 
tive conception; that is, it is either naturally positive or is 
given a positive form. In this sense, therefore, the consequent 
of the major must be positive, and (a) the major must be an 
affirmative proposition. Notwithstanding this, the major is 
sometimes essentially negative, as in the following : 

Some virtuous persons are not amiable ; 
Persons not amiable have few friends ; therefore 
Some persons with few friends are virtuous. 

In the same manner, (b) the minor premise must be construed as 
affirmative; because its consequent is to be used as antecedent 
of the conclusion. Yet this premise, also, may be essentially 
negative, as in the following : 

Some who are respected are hypocrites ; 
No hypocrites deserve respect ; therefore 
Some who do not deserve respect receive it. 

And finally, (c) the conclusion must be affirmative; because it 
has for consequent the antecedent of the major. Yet it may 
be really negative, if that antecedent is a negative conception ; 
as in the following : 

Some persons not virtuous are amiable ; 
Amiable persons have many friends ; therefore 
Some who have many friends are not virtuous. 

With regard to modality, conjunctive reciprocation imposes 
no restriction on the premises. This mode of syllogizing 
merely calls for premises which can be converted by the 



Chap. XXIII.] SYLLOGISTIC MOODS. 255 

asserted-consequent; by which method all sequences whatever 
are convertible. Hence (cl) both major and minor premise may 
be either apodeictic or contingent. But a converse produced by 
the asserted-consequent is always contingent ; and therefore — 
since nothing but contingency can come from contingency — 
(e) the conclusion of a conjunctive reciprocation must be contin- 
gent. Indeed, it is always a weak contingency, being the prod- 
uct of two contingencies. 

The style of the contingency of the conclusion, however, 
varies with the character of the premises. If the converse of 
the major be guarded against impossibility, or necessity of the 
opposite, (as happens when the major itself is so guarded,) 
and if the minor premise be apodeictic, the conclusion is guarded. 
Otherwise it is not. For example, should we say either " all 
pious persons," or, 

Some pious persons, are over-exact ; 

All over- exact people are unpleasant company ; therefore 

Some persons unpleasant in company are pious, 

the conclusion would be guarded. For, the major having been 
converted by the simple asserted-consequent and the minor 
differentially, the retained-necessitant of the minor ("over- 
exact ") binds the premises together so as to prevent an un- 
guarded conclusion. The retained-necessitant operates here 
precisely as in certain moods of the third figure, and, in this 
case as in that, the law of its operation, expressed abstractly, 
is that " whatever is contingent (or is in any other way logi- 
cally related) to any subject, is similarly related to whatever 
necessarily inheres in that subject." "Pious " being connected 
with " over-exact " by a guarded contingency, must be similarly 
related to "unpleasant company," which necessarily inheres 
in "over-exact." Were the minor premise contingent, this 
result would fail for the want of a retained-necessitant to bind 
the premises together. Hence, in affirmative reciprocation, 
(/) the conclusion is an unguarded contingency, unless the major 
premise be guarded and the minor be apodeictic. 

Combining the foregoing rules (a, b, c, d, e, /), we find that 
the major premise may be either A or /; while the minor must 



256 THE MODALIST. [Chap. XXIII. 

be A j and the conclusion I. This allows only two moods, AAI r 
IAI. But, admitting the unguarded conclusion with a con- 
tingent minor, we have two moods more, A II, III. The fol- 
lowing is in the mood III: 

Some intelligent beings are men ; 
Some men are unprincipled ; therefore 
Some unprincipled beings may be intelligent. 

12. In disjunctive syllogisms of the fourth figure (a) the 
conclusion, of course, is negative; disjunction is negation, or a 
form of negation, (b) Hence the premises must be opposite in. 
quality ; because this is always necessary in order to a negative 
conclusion. 

The modality of the premises is affected by the fact that, 
both premises have to be mentally converted; so that the subject 
of the major may become predicate of the conclusion, and the 
predicate of the minor, subject of the conclusion. This being 
so, (c) the major premise must be apodeictic, that its subject, as 
predicate of the conclusion, may have an absolute distributive 
and exclusive force. Otherwise the negation of the conclusion 
would be nugatory. For a kindred reason, (d) in case the 
major premise be affirmative, the minor must be an apodeictic 
negative. Were it a contingent negative, its converse would be 
nugatory, and without logical force. The following syllogism 
is inconclusive, because the minor premise is not apodeictic : 

All metals are minerals ; 

Some minerals are not poisons ; therefore 

Some poisons are not metals. 

But (e) if the major premise be an universal negative, the minor 
may be either apodeictic or contingent. Tor in that case the 
minor would yield a true contingent converse, and the middle 
term, if not distributed in the conversa of both premises, would. 
yet be distributed in the converse of the major. Thus, 

No negro is a Hindoo ; 

Some Hindoos are black ; therefore 

Some blacks are not negroes. 



Chap. XXIII.] SYLLOGISTIC MOODS. 257 

Combining the foregoing rules we find that the major prem- 
ise may be A or E : if it is A, the minor must be E ; but if it 
is E, the minor may be A or I. 

This allows only three pairs of premises, AE, EA, EL 
Only the first pair, after conversion, justify an universal con- 
clusion according to the consequent-consequent; in both the 
other combinations the contingent converse of the minor neces- 
sitates a contingent conclusion. We have, therefore, in all, 
three negative moods, AEE, EAO, EIO. 

The first of these may be said to express the specific prin- 
ciple that " ivhatever necessitates an entity, cannot inhere in 
whatever that entity renders impossible" Let "lion" render 
"carnivore" necessary, and let "carnivore" render "four- 
stomached " impossible ; then " lion " may be absolutely denied 
of "four-stomached." 

All lions are carnivorous ; 

No carnivore is four- stomached ; therefore 

No four-stomached animal is a lion. 

The principle of the other two moods is that " whatever renders 
an entity impossible, may be contingently denied of any consequent 
of that entity" Let " negro " render " Hindoo " impossible, 
and let " Hindoo " be antecedent, either of necessity or of con- 
tingency, to "colored"; then "negro" may be contingently 
denied of " colored." 

Both these moods are fitted to produce conclusions of guarded 
contingency ; nor is there any disjunctive mood in the fourth 
figure whose conclusions are necessarily unguarded. In this 
respect syllogisms of disjunctive reciprocation resemble those 
of the separating (or disjunctive) consequents : because, in 
each case, that same construction of premises which is neces- 
sary to produce a negative conclusion, is also fitted to produce 
a guarded conclusion. In order to either of these results, the 
premises, after being reduced to the consequent-consequent 
form by the conversion of one or both premises, must be bound 
together by a necessitant conception. This may then stand 
either as predicate of the first (or minor) premise, or as subject 
of the second (or major) premise; and in every case, while 



258 THE MODALIST. [Chap. XXIII. 

supporting a negative conclusion, it also renders a guarded 
conclusion possible. Hence there are no moods either of the 
separating-consequents, or of disjunctive reciprocation, which 
produce unguarded contingencies only. 

13. Nevertheless it is not true that no unguarded contin- 
gencies can be inferred by either of these methods. For if 
any syllogism in any figure have an unguarded contingent prem- 
ise, the conclusion must be an unguarded contingency : because 
no conclusion can be any better than any premise on which it 
depends. In all the mood-formulas considered hitherto in this 
discussion, it has been assumed that no unguarded premise is 
employed, but that every contingent premise sets forth an 
absolute possibility either of being or of not being. The 
inquiry has been, " In what cases do guarded premises produce 
a guarded conclusion, and. in what cases do they produce an 
unguarded conclusion ? " The answer to this inquiry is that 
the conclusion is guarded when there is a connective necessi- 
tant ; and unguarded when there is not. But, notwithstanding 
this answer — and whatever be the mood of a syllogism — the 
conclusion must be unguarded, if either premise is unguarded. 
For the connective necessitant — or "distributed middle term" 
— adds no new force to the premises, but simply unites them 
in such a way that there can be no subsidence to the weaker 
style of sequence. 

Syllogisms with an unguarded contingent premise may be 
neglected, and treated as exceptional, because of their rare 
occurrence ; yet they are possible in any contingent mood, of 
whatever figure. Let us take the mood EIO, in the second 
figure, and employ for minor premise the unguarded contin- 
gency, "an ox maybe a carnivore " ; inferred, because a quadruped 
may be a carnivore, and an ox is a quadruped. Let us say, 

No four-stomached animal is a carnivore ; 
An ox may be a carnivore ; therefore 
An ox may not be four- stomached. 

Here the conclusion is unguarded, not because of any laxity 
in the mood, but because of the original deficiency of the minor 



Chap. XXIIL] SYLLOGISTIC MOODS. 259 

premise. The connective necessitant "carnivore," found in the 
major premise, cannot remedy this defect. 

A precisely similar result follows in the mood EIO of the 
fourth figure, if we convert the above minor premise, and say, 

No four-stomached animals are carnivores ; 
A carnivore may be an ox ; therefore 
An ox may not be four- stomached. 

14. All the negative moods of the fourth figure employ in 
the middle places some term and its contradictory; and so 
immediately appeal to the law of Contradiction. In this par- 
ticular these moods resemble those of the separating-conse- 
quents, and are unlike those of the consequent-consequent : 
these last do not employ a term and its contradictory, but the 
very same middle conception twice. Hence we naturally reduce 
the negative moods of the fourth figure to equivalent moods 
in the second figure ; simply converting the minor premise, we 
complete the inference by the separating-consequents, without 
further conversion. 

On the other hand, the positive moods of the fourth figure 
are easily replaced by equivalent moods in the third figure, 
through a conversion of the major premise ; after which the 
mind can complete its work according to the law of the 
common-antecedent. But these positive moods of the fourth 
figure are also easily interpreted by the conversion of both 
premises, and the use of the consequent-consequent. 3STay, 
syllogisms of the third figure seem, for the most part, to be 
mentally effected by the consequent-consequent, after conver- 
sion of the minor. The law of the common-antecedent does 
not have so independent and distinctive an operation as that 
of the separating-consequents. The syllogism of the third 
figure may be explained as a variation of that of the first, 
resulting from a comparatively insignificant conversive addi- 
tion, based on the principle of identity. 

15. If these things be so, great prominence should be given 
to the methods of the consequent-consequent and of the sepa- 
rating-consequents. The one is the method of conjunctive, the 
other of disjunctive, syllogizing. In the one, a given sequence 



280 THE MODALIST. [Chap. XXIII. 

(major premise) is accompanied by the inferential assertion 
of its antecedent as the consequent of another sequence 
(minor premise) ; and thereupon the consequent of the major 
premise is asserted : this appeals to that primary use of the 
law of Reason and Consequent, according to which first the 
antecedent, and then the consequent, is asserted. In the other, 
a given sequence (major premise) is accompanied by the in- 
ferential denial of its consequent, by reason of this consequent 
being the contradictory of the consequent of another sequence 
(minor premise) ; and thereupon the antecedent of the major 
premise is denied : this appeals to that secondary use of the 
law of Antecedent and Consequent, according to which first 
the consequent, and then the antecedent, is contradicted, or 
denied. Thus the first and the second figures appeal more 
directly than the third, and much more directly than the 
fourth, to the fundamental principle of inference. 



Chap. XXIV.] THE PURE, OR DOGMATIC, SYLLOGISM. 261 



CHAPTER XXIV. 

THE PURE, OK DOGMATIC, SYLLOGISM. 

1. Is the syllogism recognized by modern authorities. Reasons about 
things as members of logical classes, and on principles relating to such 
classes. Has the same "figures" with the modal syllogism; but the 
subject of each proposition always is, and the predicate always may be, 
a class or part of a class. 2. The first figure arises when the subject of 
one premise is made the subject, and the predicate of the other premise 
the predicate, of the conclusion. It is governed by the " Dictum" ; and 
has the moods Barbara, Celarent, Darii, Ferio. 3. The second figure 
arises when the premises have contradictory predicates. Its moods are, 
Cesare, Camestres, Festino, Baroko. 4. The third figure arises when the 
premises have a common subject. Its moods are, Darapti, Datisi, Disa- 
mis, Felapton, Bokardo, Feriso. 5. The fourth figure arises when the 
predicate of one premise is made the subject, and the subject of the other 
premise, the predicate, of the conclusion. Its moods are, Bramantip, Di- 
maris, Camenes, Fesapo, Fresison. 6. Euler's diagrams. 7. Hamilton's 
syllogistic notation. 8. Its application to conjectural moods. 9. His 
multiplication of moods uncalled for. 10. The enthymeme, epicheirema, 
sorites, and polysyllogism. 

1. Pure, or dogmatic, propositions, though, in form mere 
statements of fact, really express laws of necessity and of con- 
tingency ; and their value arises from their fitness for this use. 

That they are not properly factual assertions is evident 
because the logical classes whose existence they assume are 
essentially supposed, or hypothetical, entities — creations which 
the mind makes for the purposes of its thought. When we 
say, " All men are mortal," or " Some men are wise," the class 
of which we speak includes all human beings that ever have 
been or shall be, and, in addition, all that may be supposed or 
imagined to be. Therefore, as a whole, it is hypothetical in 
character and use. 

Pure, or dogmatic, syllogisms are tJwse composed exclusively of 
pure propositions, and are the only kind recognized by modern 



262 THE MODALIST. [Chap. XXIV. 

authorities. Dr. Thomas Keid, in 1770, in his "Analysis of 
Aristotle's Organon," p asses over the rules for modal syllo- 
gisms in silence, saying that in this he follows the example 
"of all writers in logic for two hundred years back." In 1870, 
Sir Wm. Hamilton declares that " the modality of propositions 
and syllogisms ought to be wholly excluded from logic " ; and 
this is the doctrine commonly taught at the present time. The 
modal syllogism has been "formally expelled from the science," 
on the ground that it is only a modification of the pure syllo- 
gism, and should be interpreted accordingly. 

This position is the reverse of truth ; the pure syllogism is 
the secondary mode of thought, and should be interpreted by 
the modal. At the same time the importance of the pure 
syllogism cannot be denied. It is the best expression of our 
ordinary reasonings ; and it is the basis of rules which are easily 
apprehended and applied. Therefore, also, an account of it 
properly follows discussions in which the laws of the modal 
syllogism have been explained. 

The figures of the dogmatic syllogism are identical with 
those of the modal, but every proposition used in them asserts 
something respecting the whole or a part of some logical class 
considered distributively. Comparing the figures with refer- 
ence to their immediate operation, they may be named the 
subordinative, the refutative, the partitive, and the reciproca- 
tive. In the first, one truth is inferred as subordinate to 
another : in the second, a proposition is disproved by an appeal 
to the law of contradiction : in the third, something is included, 
positively or negatively, about a part of a class of things ; and 
in the fourth, a mediate predicate (or consequent) becomes 
conversely — or reciprocally — subject instead of predicate (or 
antecedent instead of consequent). Thus each figure of syl- 
logizing has a specific operation ; though it cannot be said to 
be confined to this operation as an end. 

2. The dogmatic syllogism of the first figure arises when 
the subject of one premise is made the subject, and the predi- 
cate of the other premise, the predicate, of the conclusion. It 
is governed by the principle known as " Aristotle's Dictum," 
that whatever is affirmed or denied of a generic class, distribu- 



Chap. XXIV.] THE PURE, OR DOGMATIC, SYLLOGISM. 263 

lively, may be asserted in the same ivay of any subordinate 
classes or individuals. Hence, as to quality, (a) the major 
premise may be either affirmative or negative ; (b) the minor 
must be affirmative, because it asserts membership in the 
class ; and (c) the conclusion must agree in quality with the 
major. As to quantity (d) the major must be universal; (e) 
the minor is either universal or particular, according as it 
asserts that all or a part of a class is contained in the generic 
class ; and (/) the conclusion must agree with the minor in„ 
quantity. 

Combining these rules we find that the major may be A or 
E ; the minor A or J; the conclusion A, E, I, or ; and the 
following moods are valid, AAA, EAE, All, EIO. These are 
known by the names Barbara, Celarent, Darii, and Ferio, in 
each of which the vowels of a mood are presented in their 
order. To illustrate these moods, we can say, 



in Barbara, 
in Celarent, 
in Darii, 
in Ferio, 



All trees are combustible ; 
All oaks are trees ; therefore 
All oaks are combustible ; — 

No trees are minerals ; 

All oaks are trees ; therefore 

No oaks are minerals ; — 

All oaks are deciduous ; 
Some trees are oaks ; therefore 
Some trees are deciduous ; — 

No oaks are evergreens ; 
Some trees are oaks ; therefore 
Some trees are not evergreens. 



Considered mentally, all these moods follow the law of the 
consequent-consequent. The first two have apodeictic conclu- 
sions ; the other two, contingent. But these contingent con- 
clusions are guarded against a necessity of the opposite, 
because the contingency of them is supported by fact. A 
sequence which takes place occasionally cannot be impossible. 
Hence these four pure moods agree with those four modal 



264 THE MODALIST. Chap. XXI V. 

moods, of the first figure, which produce either apodeictic 
conclusions or guarded contingencies. Or — since every apo- 
deictic statement is guarded against the opposite necessity — 
we might say that these are essentially the four guarded moods 
of the consequent-consequent. 

We should remark, however, that not every syllogism with 
a guarded contingent conclusion can be stated in pure prop- 
ositions. Only inductive, or empirical, contingency, and 
guarded conclusions from it, can be set forth dogmatically. 
If the premise be a guarded mathematical, or intuitive, con- 
tingency, both premise and conclusion call for modal expres- 
sion (Chap. XXI.). But, since the contingencies commonly 
considered are empirical, all ordinary reasoning can be pre- 
sented in pure syllogisms. 

3. Dogmatic syllogisms of the second figure are governed 
by the axiom that " if a class have any positive, or any negative, 
characteristic, universally, then any class or individual which has 
a contrary characteristic, does not belong to that class — in other 
words, does not have the essential nature of that class." Ac- 
cording to this (a) the major premise may be either affirma- 
tive or negative, (b) the minor must be opposite in quality to 
the major, (c) the conclusion must be negative. Also, (d) the 
major must be universal, (e) the minor may be either univer- 
sal or particular, and (/) the conclusion must agree in quantity 
with the minor. 

Combining these rules, we find that the major may be A or 
E; if the major is A, the minor must be E or 0, but if the 
major is E, the minor must be A or I; the conclusion must 
be E or 0; and the valid moods are EAE, AEE, EIO, AOO. 
These are known by the names Cesare, Camestres, Festino and 
Baroko (or Fakoro). Thus we may say, 

in Cesare, 

No sound is visible ; 

All color is visible ; therefore 

No color is a sound ; — 
in Camestres, 

All color is visible ; 

No sound is visible ; therefore 

No sound is a color ; — 



Chap. XXIV.] 1HE PURE, OR DOGMATIC, SYLLOGISM. 265 

in Festino, 

No vices are praiseworthy ; 

Some habits are praiseworthy ; therefore 

Some habits are not vices ; — 

in Baroko, 

All birds are oviparous ; 

Some animals are not oviparous ; therefore 

Some animals are not birds. 

A slight inspection shows that the above moods really follow 
the law of the separating-consequents. They are, therefore, 
of the same nature with those four modal moods in which 
guarded conclusions are drawn in the second figure. 

4. Dogmatic syllogisms in the third figure are best explained 
by a double law, consisting of two axioms. First, "if tiuo 
predicates be affirmed of the same class of tilings, one of the pred- 
ications, at least, being universal, then either predicate may be 
particularly asserted of the other, that is, of the class which the 
other designates" In other words, if one predicate be with all 
the members of a class, and another either with some or with 
all, each of these predicates must sometimes be with the other. 

This principle calls for two affirmative premises, one of 
these, at least, being universal; and a particular affirmative 
conclusion. Therefore the major may be A or i", and the 
minor A or I, but if either premise be /, the other must be A ; 
the conclusion must be i"; and the valid moods are AAI, All, 
IAI. These are named Darapti, Datisi, and Disamis ; and 
they are mentally identical with those affirmative moods of 
the common-antecedent which have guarded conclusions. 

The second axiom is that "if one predicate be denied and 
another affirmed of the same class of things, one of the predica- 
tions, at least, being universal, then the predicate denied may be 
particularly denied of the other, that is, of the class designated by 
the other." For, on the one hand, what is separate from every 
member of a class, must be separate from what inheres in the 
members of that class as often as this inherency exists ; and, 
on the other hand, what is separate from a part of a class, 
must be sometimes separate from that which inheres in every 
member of that class. 



266 THE MODALIST. [Chap. XXIV. 

According to this (a) the major premise must be negative — 
it asserts separation from a class of things : (b) the minor 
must be affirmative — it asserts union with that class; and 
(c) the conclusion is negative. Also (d) the major must be 
universal if the minor is particular — otherwise it may be 
particular ; (e) the minor must be universal if the major is 
particular — otherwise it may be particular ; and (/) the con- 
clusion must be particular. Hence, under the limitations of 
these rules, the major may be E or 0, and the minor A or J; 
the conclusion must be 0; and the valid moods are EAO, 
OAO, EIO. These are known by the names Felapton, Bo- 
kardo (or Dokamo) and Feriso ; and they agree with the neg- 
ative moods of the common antecedent which have guarded 
conclusions. 

Thus dogmatic syllogisms in the third figure have three 
affirmative moods, and three negative. We can say, 



in Darapti, 



in Datisi, 



All gilding is metallic ; 

All gilding shines ; therefore 

Some shining things are metallic ; — 



All homicides are cruel ; 

Some homicides are lawful ; therefore 

Some lawful things are cruel ; — 



in Disamis, 

Some homicides are lawful ; 

All homicides are cruel ; therefore 

Some cruel things are lawful ; — 

in Felapton, 

No moral precept is a material thing ; 
All moral precepts are useful ; therefore 
Some useful things are not material ; — 

in Bokarclo, 

Some fevers are not infectious ; 
All fevers are diseases ; therefore 
Some diseases are not infectious ; — 



Chap. XXIV.] THE PURE, OR DOGMATIC, SYLLOGISM. 267 

in Feriso, 

No punishments are pleasant ; 

Some punishments are beneficial ; therefore 

Some things beneficial are not pleasant. 

5. Dogmatic syllogisms in the fourth, figure are most natu- 
rally explained by three axiomatic principles. 

The first of these pertains to affirmative syllogisms, and is, 
that "if a first class be partly, or ivholly, included in a second, 
and the second wholly in a third, then that third is partly com- 
prised in the first." If all or some P's be M's, and all M's be 
S's, then some S's must be P's. According to this the major 
must be A or I; the minor A ; the conclusion J; and we have 
two valid moods, AAI, IAI. These are called Bramantip and 
Dimaris ; they agree with the guarded moods of affirmative 
reciprocation (Chap. XXIII.). 

We need scarcely say that the P's, the M's, and the S's men- 
tioned above are the classes of things characterized by the 
major, the middle, and the minor terms respectively ; for the 
major term is the predicate, and the minor the subject, of 
the conclusion in every syllogism. 

The second axiom justifies an universal negative conclusion. 
It is that "if a first class (P's) be wholly included in a secoyid 
(M's), which is ivholly excluded from a third (S's), then the 
third is ivholly excluded from the first." This principle is the 
dogmatic expression of the law of absolute disjunctive recip- 
rocation. It supports only one mood, AEE; and this has been 
named Camenes. 

The third axiom justifies particular negative conclusions. 
"If a first class (P's) be ivholly excluded from a second (M's), 
which is wholly or partly included in a third (aS"s), then the third 
must be partly excluded from the first." Evidently this prin- 
ciple supports two moods, EAO, EIO\ and these, which are 
known as Fesapo and Fresison, are substantially those of con- 
tingent disjunctive reciprocation. 

Thus, in the fourth figure, the dogmatic syllogism has two 
affirmative and three negative moods. We can say, 



268 THE MODALIST. [Chap. XXIV. 

in Bramantip, 

All greyhounds are dogs ; 

All dogs are quadrupeds ; therefore 

Some quadrupeds are greyhounds ; — 

in Dimaris, 

Some virtuous men are necessitarians ; 

All necessitarians are speculators ; therefore 

Some speculators are virtuous men ; — 

in Camenes, 

All ruminants have four stomachs ; 

No four- stomached animal is carnivorous ; therefore 

No carnivore is ruminant ; — 

in Fesapo, 

No negro is a Hindoo ; 

All Hindoos are colored ; therefore 

Some colored men are not negroes ; — 

in Fresison, 

No moral motivity is an animal impulse ; 

Some animal impulses are principles of action ; therefore 

Some principles of action are not moral motivities. 

The fourth figure and its rules employ a mode of thought 
which, is possible in every figure, but which is less called for 
and less natural in the other figures than in the fourth. Very 
frequently, in syllogizing, we substantialize and quantify only 
two of the three terms, and use the third term in an adjective 
way ; that is, we conceive of two classes and of an ascriptive 
predicate. But, in every pure proposition, the predicate as well 
as the subject may be quantified and may be taken to represent 
the whole or part of a class ; so that every dogmatic syllogism 
may be stated as setting forth three logical classes, with cer- 
tain relations between them of inclusion and of exclusion. 

6. In connection with this mode of conception, diagrams 
have been employed to illustrate the moods of pure syllogisms 
by means of plane figures. In Euler's "Letters to a German 
Princess," a circle is used to symbolize the class of things 
designated by a term. The universal affirmative proposition 
is indicated by completely enclosing a subject-circle within a 
predicate-circle ; the particular affirmative by a subject-circle 



Chap. XXIV.] THE PURE, OR DOGMATIC, SYLLOGISM. 269 



which is partly included in the predicate-circle ; the universal 
negative by a subject-circle which is completely excluded from 
the predicate-circle ; and the particular negative by the same 
diagram as the particular affirmative, but with the understand- 
ing that the subject-circle is partly excluded from the predi- 
cate-circle. 

These symbols do not serve so well for particular as for 
universal assertions ; because they show to the eye only that 
"some" are, or are not, without adding that "perhaps all" 
are, or are not. This, however, being understood, every mood 
in every figure may be represented geometrically. For exam- 
ple, in the fourth figure, the mood Bramantip, which asserts 

that 

All P is M- 

All M is 8 ; therefore 

Some S is P — 

assumes visible shape when we indicate the major premise by 

enclosing a first circle in a second, and the 

minor by enclosing that second in a third. 

For then these circles show plainly that 

some of S must be P. This same diagram may 

set forth Barbara of the first figure. Only, 

for this end, the intermediate-circle should 

be drawn first, the outer one second, the 

innermost last; and the letters Pand S should exchange places. 

Dimaris, in the fourth figure, is diagrammed by first draw- 
ing the circle P so as to intersect the circle M ; this expresses 
the major premise ; then, by 
circumscribing M with an- 
other circle S, we express 
the minor premise. Thus it 
is made to appear that some 
#'s must be Ps. 

This same diagram, with- 
out any change, illustrates 
Disamis, of the third figure, 
if we first draw M, then P, 
and then S. For then we can say, 






270 THE MODALIST. [Chap. XXIV. 

Some Mis P; 

All Mis S; therefore 

Some S is P. 

Again, Camenes, of the fourth figure, is explained, if we 

draw one circle within a second, to 
represent the inclusion asserted in 
the major premise ; and then a third 
circle outside of the second, to rep- 
resent the exclusion asserted in the 
minor premise. Plainly no S's are P's. 

This diagram, without any change, serves for Camestres of 
the second figure ; which indicates that Camestres and Camenes 
differ very little. 

Should we neglect the lettering, one diagram will represent. 
Celarent, Cesare, Camestres, and Camenes ; one, also, will suf- 
fice for Darii, Disarms, Datisi, and Dimaris; and another,, 
varying but slightly from this, will express Darapti. One will 
be sufficient for Ferio, Festino, Feriso, and Fresison ; , and 
another, differing little from this, for Felapton and Fesapo. 
We have already seen that one serves for Barbara and Bra- 
mantip. This community in symbolization suggests, what 
investigation shows to be the fact, that different sets of moods 
have a radical sameness of nature and operation. 

Other symbols than plane figures have been used for the 
ocular illustration of propositions and syllogisms. The Ger- 
man logician, Lambert, and after him Sir William Hamilton, 
employed parallel lines ; but this plan proved difficult of appli- 
cation in the subordinate figures. 

7. Then Sir William Hamilton devised an excellent notation, 
in which propositions (not terms) are represented by hori- 
zontal lines thickened at the subject end, and sharpened at the 
predicate end; terms are indicated by letters; the distribution 
of a term by the addition of a colon ; and its non-distribution 
by a comma. Affirmation is expressed simply by the line;, 
negation by the line with a dash across its centre. 

?:■ , ,S 

means "All P's are (some) S's," and is equivalent to A. 



Chap. XXIV.] THE PURE, OB DOGMATIC, SYLLOGISM. 271 

P:— I :S 

means " Ko P is (any) S" and is equivalent to E. In stating 
syllogisms, we first place the middle term (that is, a letter 
indicating it) in the middle, the minor on the right, and the 
major on the left ; then insert the proper marks between each 
extreme and the middle ; and, finally, draw a long line, either 
above or below, to indicate the conclusion. 
Barbara is expressed thus : 



P. — M ^^^^:S 

For this, in accordance with the explanations given above, reads, 

All M are P ; 

All S are M ; therefore 

All S are P. 

As the letters at the extremities of the conclusion-line are 
always repeated from the premises and can be easily under- 
stood, they may as well be omitted. So also may the marks 
of quantity except when a term loses in the conclusion the 
distribution which it had in the premise. In the foregoing 
symbolization, the conclusion-line would be sufficient alone, 
but in that for Bramantip a new sign must be used at the 
predicate end of the line ; thus, 



For this now reads, according to the order of the fourth figure, 
All Pare M ; 
All M are S ; therefore 
Some S are (some) P. 

Festino, of the second figure, is written thus : 

Pf I | :M, — ,S 



for this reads, 

No P are (any) M ; 

Some S are (some) M ; therefore 

Some S are not (any) P. 

According to this admirable notation, the nineteen dogmatic 
moods are represented as follows : 



272 



THE MODALIST. 



Barbara, p 



Celarent P:- 




Darapti P, 



Disamis P, 



Datisi P,- 



Felapton P: 



:M: 



Bokardo P: 



,M: 



Feriso P:- 



M, 



Chap. XXIV.] THE PURE, OR DOGMATIC, SYLLOGISM. 273 

Figure IV. 
Bramantip P : 1^^^— , M : i^m— — , S 



Dimaris P,I^ ,M: ^m^^—~,& 



Camenes P:^»»^— ,M: 
I 



Fesapo P:i^»|— — :M: »^»— , S 

1 

Fresison P:»i^»^— :M, ■hm^~— ,S 



8. The twelve contingent moods with unguarded conclusions, 
which the doctrine of modality adds to the nineteen moods 
which are capable of dogmatic expression, may be set forth 
by the above symbolization provided a very elongated triangle 
take the place of the thick tapering line in representing the 
conclusion. For example, in the first figure we would have, 

IAI P, M ,M, 



For we can say, 



Some uncivilized people are treacherous ; 
The Hottentots are uncivilized ; therefore 
A Hottentot may be treacherous. 



In the second figure we might have 
AAI P:W ,M, 



and so on with the rest of the twelve moods. The commas in 
the conclusions of these moods indicate contingency, not 
particular quantity; and they might be omitted; for every 
conclusion is contingent. 

Moreover, the unguarded contingent premises, which we 
sometimes use, might also be indicated by the elongated tri- 



274 THE MODALIST. [Chap. XXIV. 

angle; and in this way the purest form of conjectural syllo- 
gizing could be symbolically represented. 

9. Sir William Hamilton uses his notation to set forth all 
those dogmatic moods which his "thorough-going quantifica- 
tion of the predicate" renders possible. He claims that, 
besides A, E, I, and 0, four other styles of propositions are 
often — and ordinarily — employed; viz., the universal-universal 
affirmative, U, "all is all"; the particular-universal affirmative, 
T, " some is all " ; the universal-particular negative, rj, " all is 
not — or none is — some " ; and the particular-particular nega- 
tive, o), "some is not some." After these are mingled with 
A, E, I, and 0, we can construct twelve affirmative and twenty- 
four negative moods in each figure; and so have in all one 
hundred and forty-four moods. 

But none of the moods added by Hamilton's scheme to those 
previously recognized, should be numbered among regular logi- 
cal forms. If either ^orw be- used as a premise, the syllogism 
is abortive because of a negative conclusion with undistributed 
predicate. For example, combining rj and A in the first figure 
we have the mood yjAtj ; thus, 

No quadrupeds are some animals ; 

All horses are (some) quadrupeds ; therefore 

No horses are some animals. 

This conclusion fails to characterize either positively or nega- 
tively ; and so does every conclusion dependent on -q or w. 

Then the use of U or Y as a premise is an extraordinary 
occurrence, and should be treated as exceptional. Ordinarily 
— always, except after certain necessary mental conversions — 
we neglect the quantity of the predicate of an affirmative 
premise. For both apodeictic and contingent affirmations are 
fully expressed without such quantification. 

Hamilton's multiplication of moods sprang from the theory 
that the essential aim of syllogizing is to show how far one 
logical class includes, or excludes, another; whereas it is to 
show whether, and in what way, the subject of the conclusion, 
as antecedent, may be related to the predicate of the conclusion, 
as consequent. 



Chap. XXIV.] THE PURE, OB DOGMATIC, SYLLOGISM. 275 

10. In connection with the pure syllogism certain terms 
may be defined, which are used chiefly to describe contracted 
modes of argument. 

When only one premise of a syllogism is expressed, the 
other being understood, the argument is called an enthymeme. 
This is of the first order, if the major premise be omitted ; 
as when we say, " Comets are subject to gravitation ; because 
they move in elliptic orbits " : and it is of the second order, 
when the minor premise is suppressed ; as when we say, 
"Comets obey the law of gravitation; because all bodies 
which move in elliptic orbits, are subject to that law." 

When an enthymeme is used as the premise of a syllogism, 
the argument is styled an epicheirenia ; and an epicheirema 
is double when both of its premises are enthymematic ; and 
single, if only one of them have that character. The follow- 
ing is a single epicheirema; in which the minor premise is 
an enthymeme of the first order : 

All vice is odious ; 

But avarice is a vice ; for it depraves men ; therefore 

Avarice is odious. 

The sorites, or chain-argument {die schluss-kette) , is the 
abbreviated statement of a series of syllogisms formed imme- 
diately according to the consequent-consequent, and belonging, 
therefore, to the first figure. It consists of a succession of 
catenated sequences ; and terminates with the conclusion that 
the consequent (or predicate) of the last proposition, follows 
the antecedent (or subject) of the first. In addition to the 
first premise and the conclusion, the sorites has as many 
propositions as it contains middle terms. 

The following is a chain of reasoning, quoted by Sir William 
Hamilton from Seneca : 

He who is prudent is temperate ; 

He who is temperate is constant ; 

He who is constant is unperturbed ; 

He who is unperturbed is without sorrow ; 

He who is without sorrow is happy ; therefore 

The prudent man is happy. 



276 THE MODALIST. [Chap. XXIV. 

This argumentation, following the natural, not the dialectic, 
order of reasoning, first makes what is to be the subject of 
the conclusion antecedent to a middle term ; then it makes 
that middle term antecedent to a second; and that second 
middle term antecedent to a third; and so on, till the last 
premise makes the last middle term antecedent to that which 
is to be the predicate of the conclusion : whereupon the con- 
clusion is asserted. This reasoning is easily resolved into the 
following syllogisms of the first figure ; in each of which the 
minor premise is written first : 

(a) He who is prudent is temperate ; 

He who is temperate is constant ; therefore 
He who is prudent is constant. 

(5) He who is prudent is constant ; 

He who is constant is unperturbed ; therefore 
He who is prudent is unperturbed. 

(c) He who is prudent is unperturbed ; 

He who is unperturbed is without sorrow ; therefore 
He who is prudent is without sorrow. 

(c?) He who is prudent is without sorrow ; 

He who is without sorrow is happy ; therefore 
The prudent man is happy. 

The above order of syllogisms — as well as that of the prem- 
ises in each syllogism — is called the progressive ; because, 
beginning with what is to be the antecedent of the conclusion, 
it follows the links of the chain (that is, the middle terms) from 
the antecedent-end to the consequent-end. It is distinguished 
from the regressive order ; according to which single syllogisms 
of the first figure are commonly stated ; and which begins with 
the consequent-end, and therefore with the major premise. 

The first of the five premises in the foregoing sorites may 
be termed the minor ; because it contains the minor term, the 
subject of the conclusion : the last of the five, the major ; be- 
cause it contains the major term : the rest of the five are 
neither minor nor major, but simply middle premises ; which, 
however, act as major premises when the series of syllogisms 
is developed. 



Chap. XXIV.] THE PURE, OR DOGMATIC, SYLLOGISM. 277 

The rules governing the sorites are entirely analogous to 
those of the first figure ; and are as follows : 

(a) Only the minor premise may be particular (or contin- 
gent) ; the rest must be apodeictic. 

(b) Only the major premise may be negative ; the rest must 
be affirmative. 

(c) The conclusion agrees in modality with the minor prem- 
ise ; and in quality with the major. 

But the first of these rules is necessary only when the con- 
clusion is to be guarded against a necessity of the opposite ; a 
series of compounded probabilities may be set forth in a chain- 
argument, and may have an unguarded conclusion. 

While the progressive is the natural order of thought for 
a sorites, the regressive order, also, may be used. We can 

say: 

He who is without sorrow is happy ; 

He who is unperturbed is without sorrow ; 

He who is constant is unperturbed ; 

He who is temperate is constant ; 

He who is prudent is temperate ; therefore 

The prudent man is happy. 

The argumentation, as thus stated, may be developed into the 
following syllogisms ; in each of which the major premise is 
put before the minor : 

(a) He who is without sorrow is happy ; 

He who is unperturbed is without sorrow ; therefore 
He who is unperturbed is happy. 

(6) He who is unperturbed is happy ; 

He who is constant is unperturbed ; therefore 
He who is constant is happy. 

(c) He who is constant is happy ; 

He who is temperate is constant ; therefore 
He who is temperate is happy. 

(d ) He who is temperate is happy ; 

He who is prudent is temperate ; therefore 
The prudent man is happy. 

In the above syllogizing Ave begin with the major term, and 
carry it backwards through the series, till it is connected with 



278 THE MODALIST. [Chap. XXIV. 

the minor j whereas the other mode of syllogizing began with 
the minor term, and carried it forwards through the series, 
till it was connected with the major. 

Rudolphus Goclenius, of Marburg, a distinguished professor 
of logic in the seventeenth century, called attention to the 
regressive sorites, and to its conformity with ordinary syllo- 
gistic formulas. Hence this form of statement has been 
named the Goclenian sorites. 

When the conclusion of a first syllogism becomes the prem- 
ise of a second syllogism, the relation between the arguments 
is indicated by calling the first a prosyUogism, and the second 
an episyllogism. This is especially the case when the conclu- 
sion of the first syllogism is the only premise required for the 
second syllogism ; the other having been already provided. 
When a sorites is developed into syllogisms, every one of 
these, except the last, is a prosyUogism, with reference to 
the succeeding syllogism; and every one except the first, is 
an episyllogism, with reference to the one preceding it. The 
whole series of syllogisms has also been called, sometimes, a 
poly 'syllogism. 



Chap. XXV.] REDUCTION OF SYLLOGISMS. 279 



CHAPTER XXV. 

REDUCTION OF SYLLOGISMS. 

1. The four figures as related to each other, and to the law of the 
consequent-consequent. 2. All logicians have followed the methods of 
Aristotle in his syllogistic "reductions." A new, and natural, method 
proposed. 3. The ordinary reductions are often artificial and indirect. 
The mnemonic mood-names. The significance of their vowels. 4. The 
significance of their initial consonants, and of the letters s, p, m, and k. 
The expressions "per accidens" and "per se." 5. Reduction "perim- 
possibile," or "per contradictionem." 6. Exercises in syllogistic con- 
struction and reduction. 7. Also in forming and reducing unguarded 
syllogisms. 

I. 1 The law of the first figure is that " if a first thing (minor 
term) be antecedent to a second (middle term), and this second 
to a third (major term), then also the first is antecedent to the 
third." We call this " the consequent-consequent" ; because the 
third thing, as being consequent to the second, is consequent 
to the first, and so becomes a consequent-consequent. It might 
also be named the consequent-consequence ; because the conse- 
quence — or sequence — in which the third thing follows the 
first, is consequent upon the combination of the two premises, 
or prior sequences. 

The law of the second figure is that if a first thing (minor 
term) have a second thing as either a positive or a negative con- 
sequent (middle term), and a third thing (major term) be neces- 
sarily followed by the contradictory of that consequent (middle 
term), then the first thing is antecedent of denial to the third. If 

1 In these discussions it must be remembered that the major term is 
always the predicate of the conclusion, and the minor term the subject of 
the conclusion ; and then that the major premise is always that which con- 
stains the major term, and the minor premise is that which contains the 
minor term. The order in which premises are stated determines nothing 
as to either figure or mood. 



280 THE MODALIST. [Chap. XXV. 

A be followed by B, and C necessarily by not-B; or if A be 
followed by not-B, and C necessarily by B ; in either case, A 
is followed by not-(7. This is the principle of "the separating- 
consequents " ; it might also be named the law of consequent 
contradiction, or denial. It is constituted by uniting to the 
syllogistic law of the consequent-consequent the conversional 
law of the denied-consequent. For when the sequence which 
must have the necessary consequent, that is, the major premise, 
is converted by the denied-consequent, the argument immedi- 
ately falls into the first figure. Thus the syllogism, 

No Germans are black (minor premise) ; 

All negroes are black (major premise) ; therefore 

No Germans are negroes, 

by the conversion of the major, becomes, 

A German is not black ; 

He who is not black is not a negro-; therefore 

No German is a negro. 

But this conversion, which is required by the separatihg- 
consequents, is in most cases potential — not actual; for, by 
an acquired habit, we can immediately deny the one antecedent 
of the other. Nor is the cogency of the argument increased by 
the change from the second figure to the first. 

The law of the third figure is that " if two consequents have 
a common antecedent (middle term), either may be contingently 
asserted of the other" This law is accounted for by combining 
with the law of the consequent-consequent the conversional law 
either of the asserted-consequent or of the retained-necessitant ; 
the latter of these being a specific mode of the former. But 
while the second figure implicitly converts the major premise, 
the third figure calls for a converted minor. Thus the syllo- 
gism (of the mood Datisi), 

All homicides are cruel ; 

Some homicides are lawful ; therefore 

Some lawful things are cruel, 

assumes the first figure on the conversion of the minor premise 
by the asserted-consequent. 



Chap. XXV.] REDUCTION OF SYLLOGISMS. 281 

But, in the syllogism (in Disamis), 

Some homicides are lawful ; 

All homicides are cruel ; therefore 

Some cruel things are lawful, 

we must convert by the retained necessitant ; thus, 

Some homicides are lawful ; 

Some cruel things are all the homicides ; therefore 

Some cruel things are lawful. 

So, also, the following (in the mood Bokardo) 

Some writers on logic are not clear thinkers ; 

But all writers on logic profess to teach the laws of thought ; therefore 

Some who profess to teach the laws of thought, are not clear thinkers , 

on converting the minor, becomes 

Some writers on logic are not clear thinkers ; 

But some who profess to teach the laws of thought, are all the writers on 

logic ; therefore 
Some who profess to teach the laws of thought, are not clear thinkers. 

In the above reductions — of Disamis and Bokardo — the 
retained necessitant is necessary, in order that the conclusion 
may not become unguarded. In Darapti and Felapton, also, 
the minor premise may be converted by the retained necessi- 
tant ; but this is not needed for a guarded conclusion ; the 
asserted consequent is sufficient; though the conclusion thus 
obtained in these moods is not so strong as that which would 
follow the retained necessitant. 

The operation of the third figure is closely allied to that of 
the first. Its conversions suggest themselves more easily than 
those of the second figure ; these latter are driven back from 
prominence by the action of the principle of contradiction. 
In the course of discussion an argument gi^en in the third 
figure is often spontaneously restated in the first ; this seldom 
happens with an argument in the second figure. Yet the 
third figure, as well as the second, has an independent opera- 
tion. 

The fourth figure has less independence than either the 
second or the third ; and also less unity of principle. It has 



282 THE MODALIST. [Chap. XXV. 

three laws, one for conjunctive, and two for disjunctive, recip- 
rocation (Chap. XXIV.)- 

Though this figure may at times operate independently, 
probably most arguments in it are effected by a mental conver- 
sion which reduces the syllogism to one of the other figures. 
Two conversions reduce any mood to the first figure ; but the 
negative moods naturally fall into the second figure by con- 
verting the minor premise, and the positive moods into the 
third by converting the major (Chap. XXIII.). 

2. Aristotle discusses only three figures, probably discarding 
the fourth as merely an irregular derivative from the others. 
For, if we take either Bramantip, Dimaris, or Camenes ; and — 
what is merely a matter of order — transpose the premises of 
the mood ; we obtain a conclusion in the first figure, of which 
the conclusion in the fourth figure is the converse : if we take 
either Camenes, Fesapo, or Fresison (the negative moods) ; 
and convert only the minor premise; we obtain the very 
same conclusion in the second figure, as in the fourth:, and, if 
we take either Bramantip or Dimaris (the affirmative moods) ; 
and convert the major premise ; we obtain the very same con- 
clusion in the third figure, as in the fourth. Moreover, every 
one of these reductions improves the statement of the argu- 
ment. This fact shows the inferiority of the fourth figure; 
and explains, though it does not wholly justify, the neglect of 
that style of syllogizing, by Aristotle and others. 

The fourth figure has been ascribed to Galen, who lived in 
the second century of the Christian Era, but, according to Sir 
William Hamilton, it is first mentioned by Averroes, who lived 
in the twelfth century. 

Aristotle proved the validity of reasonings in the second and 
third figures by showing that they are equivalent to reasonings 
in the first ; and all subsequent logicians have felt bound to 
reduce the moods of each subordinate figure to equivalent 
moods in the first figure. 

This reduction would present no difficulty, if it were only 
borne in mind that the universal, or apodeictic, affirmative 
may be converted in any one of three ways ; either by the 
asserted-consequent (per accidens), or by the retained-necessitant 



Chap. XXV.] REDUCTION OF SYLLOGISMS. 283 

(per differentiam), or by the deniecl-con sequent (per contradic- 
tionem). We must also remember that the apodeictic nega- 
tive can be converted by the denied-consequent ; the contingent 
affirmative, by the asserted-consequent ; and that the particular 
negative is not to be converted at all. With these rules any 
mood in a subordinate figure can be immediately reduced to 
the first figure, without any change in the order of its prem- 
ises, and without any alteration whatever in the conclusion. 

In every mood of the second figure we simply convert the 
major by the denied-consequent. In this way, for example, Ba- 

roko, 

All birds are oviparous ; 

Some animals are not oviparous ; therefore 

Some animals are not birds, 

becomes Eerio, 

No non-oviparous are birds ; 

Some animals are non-oviparous ; therefore 

Some animals are not birds. 

In the third figure we convert the minor by the asserted-con- 
sequent; or by the retained-necessitant, if the case so require. For 
when only the minor premise is apodeictic, the full distributive 
force of its antecedent must be retained : otherwise the con- 
clusion would not be a guarded contingency. This has been 
exemplified above (Chap. XXIV.). 

The fourth figure is immediately reduced by converting both 
premises. For example, the mood Camenes, 

All ruminants are four- stomached ; 

No four-stomached animal is a carnivore ; therefore 

No carnivore is a ruminant, 

becomes, by the retained-necessitant and by the denied-conse- 
quent, the mood YEE, in the first figure. 

Some four-stomached are all the ruminant ; 
No carnivore is four-stomached ; therefore 
No carnivore is a ruminant. 

In like manner, every mood in this figure may be reduced by 
two conversions. 



284 THE MODALIST. [Chap. XXV. 

Reductions, after the manner now proposed and explained, 
accord with the philosophy of the syllogism and its figures ; 
and should satisfy those who recognize that the universal 
affirmative can be converted in three ways. , 

3. But, till recent times, logicians have subjected this style 
of proposition only to one method of conversion; that is, to 
conversion "per accidens," or "by limitation," or, more abso- 
lutely speaking, by the asserted-consequent. Under this 
restriction the reduction of syllogisms was attended with 
difficulties. Indeed, seven, out of the fifteen moods of the 
subordinate figures, proved irreducible. It was found possible, 
however, to reach the conclusions of these moods through the 
first figure by more or less " indirect " reductions — in other 
words, by processes which involve the aid of supplementary 
devices. 

For the correct performance of the reductions thus brought 
into use certain rules were found necessary ; and these have 
been compactly preserved for us in the famous lines of. Petrus 
Hispanus, who lived in the fourteenth century, and who is 
known also as Pope John XXII. : 

Barbara Celarent Darii Ferioque prioris ; 
Cesare Camestres Festino Baroko secundas ; 
Darapti Disamis Datisi Felapton Bokardo 
Feriso sunt sex modi Tertise. Quarta insuper addit 
Bramantip Dimaris Camenes Fesapo Fresison. 

This list includes all dogmatic moods which can be constructed 
with A, E, I, and 0; and therefore, modally speaking, all ordi- 
nary moods which are either apodeictic or of a guarded con- 
tingency. Moods with an unguarded conclusion were rejected 
because they cannot be expressed dogmatically ; and are, also, 
in a certain sense, inconclusive. 

The ingenuity of the mnemonic lines lies in the names given 
to the moods. 

The character of each mood as to the quality and quantity, 
or modality, of its propositions, is indicated by the three vowels 
which its name contains. In Darii, for example, of the first 
figure, or in Datisi, of the third, the major must be an universal 



Chap. XXV.] SEDUCTION OF SYLLOGISMS. 285 

affirmative; the minor, a particular affirmative; and the con- 
clusion, a particular affirmative. 

4. Again, the names of the four moods of the first figure 
begin with the first four consonants of the alphabet ; and the 
name of every mood in each of the other figures also, begins 
with one or other of these letters. This informs us to what 
mood in the first figure any mood in a subordinate figure is to 
be reduced. Camestres is to be reduced to Celarent ; Felapton 
to Ferio. 

Further, while only the initial consonants are significant in 
the first figure, in the other figures practical directions are 
given by means of the letters s, p, m, and k. S, which is 
inserted only after E or I, signifies that the proposition which 
it follows is to be converted " simply," or without change in 
quality or quantity : in Fresison both major and minor are to 
be converted simply. 

Only E and I can be converted in this way. This does not 
mean, however, that both these conversions take place on the 
same principle ; for the conversion of E follows the denied- 
consequent, while that of I follows the asserted-consequent. 
Moreover, the operation of these laws is " simple " only in the 
sense of being intelligible. In the one case the absolute denial 
of an antecedent follows the contradiction of its necessary con- 
sequent ; in the other an antecedent of contingency is contin- 
gently asserted, on its consequent being assumed to exist. 

The explanation of the conversion of E by the mutual ex- 
clusion of two classes, and of I by the reciprocity of partial 
inclusion between two classes, is also simple ; but only super- 
ficially. Nothing is truly and philosophically simple which 
cannot be understood without further explanation. The mutual 
exclusions and inclusions of logical classes are only a mental 
device for vividly expressing reciprocations of impossible and 
of contingent sequence. 

The 'letter p, when it follows the vowel A, signifies that the 
apodeictic affirmative is to be converted "per accidens" ; or, as 
we would prefer to say, by the asserted-consequent, and on 
the principle of the contained-conditions (Chap. XXI.). This 
conversion is of the same nature with that of the particular, 



286 THE MODALIST. [Chap. XXV. 

or contingent, affirmative. But it differs from the latter in 
that the antecedent of the convertend, which contains a neces- 
sitating condition of the consequent, after becoming predicate 
of the converse, drops its necessitant and distributant force; 
although this might have been retained. We convert "man 
must die" into "what dies may be a man," when, were the 
full force of the convertend retained, we would say, " Only 
what dies — or is mortal — can be human." 

Conversion per accidens was formerly confined to the apo- 
deictic affirmative ; but it is applicable to the universal negative 
as well. "No fishes are viviparous," yields "some animals not 
viviparous are fishes " ; and, for the same reason — that is, 
because of the law of contained-conditions in its negative 
operation (Chap. XXI.), the particular negative may be con- 
verted in the same way. "A fish may not be a marine animal," 
yields "what is not a marine animal may be a fish." 

In saying that A is converted "per accidens" the Latin 
logicians contrasted the modality of the converse with that of 
the convertend. In the latter, consequent follows antecedent 
universally (kol06\ov), necessarily (e| dvay/c^s), or per se (ko.0' 
avrb) ; in the former, particularly (£v /xepei), contingently (ivSexo- 
(Atvois), or per accidens (Kara ^^jStjkos) — in each case the 
same mode of sequence being viewable in either of three ways. 
" Universally " and "per se " are secondary modes of stating 
necessity ; " particularly " and "per accidens " are secondary 
expressions of contingency. Man "per se," or necessarily, is 
a mortal and a terrestrial being ; but "per accidens," or con- 
tingently, he is a wise being, or an Asiatic. 

In this connection, "per se " does not mean " by a nature, or 
essence, alone," but " by a nature under any circumstances what- 
ever"; and "per accidens" does not mean "without the 
nature," but rather " by means of the nature under these cir- 
cumstances; or under those." (Vide Arist., " Analyt. Post.," 1. 4.) 

The letter " m," in the mnemonic names, calls for a mutation, 
or transposition, of the premises ; so that the major becomes 
minor, and the minor, major. This was found unavoidable in 
five moods. But the major premise furnishes the predicate, 
and the minor premise the subject, of the conclusion ; therefore 



Chap. XXV.J REDUCTION OF SYLLOGISMS. 287 

the transposed premises, though they bring the argument into 
the first figure, do not produce the original conclusion, but 
only a conclusion from which the original can be obtained by 
conversion. For example, the following, in Camestres, 

All color is visible ; 

No sound is visible ; therefore 

No sound is a color, 

becomes, in Celarent, 

Nothing visible is a sound ; 
All color is visible ; therefore 
No color is a sound ; 

in which the conclusion is convertible into the original con- 
clusion. Hence the final s, in the mood-name. 

Aristotle himself reduces Camestres in this way ; and indeed 
all the rules of Hispanus simply embody the methods of Aris- 
totle. ("Analyt. Prior.," I. 5.) 

Here it should be noticed that p in Bramantip does not 
indicate the conversion of /, but of A so as to produce I. For 
the transposed premises produce a syllogism in Barbara. 

5. Finally, "fc" signifies that the mood is to be reduced 
"per impossibile," that is, by an appeal to the principle of 
contradiction. Two moods, Baroko and Bokardo, defeated all 
attempts to reduce them, either directly or with mutation of 
premises. If, however, we substitute, for the premise which 
"k" follows, the contradictory of the conclusion, and retain 
the other premise, we can obtain a syllogism of the first figure. 
The conclusion of this syllogism will be the contradictory of 
the suppressed premise ; and therefore, as contradicting what 
was laid down at the beginning, cannot be true. But, as this 
false conclusion results simply from using the contradictory 
of the conclusion as a premise, that contradictory must be false; 
and the original conclusion, which it contradicts, must be true. 

In Baroko we say, 

All birds are oviparous ; 

Some animals are not oviparous ,' therefore 

Some animals are not birds. 



288 



THE MODALIST. 



[Chap. XXV. 



Substituting for the minor the contradictory of the conclusion^ 

we have 

All birds are oviparous ; 

All animals are birds ; therefore 

All animals are oviparous. 

But this conclusion is the contradictory of the original minor,, 
and must be false ; therefore the substituted premise must be 
false, and its contradictory, the original conclusion, must be true. 

A precisely similar proof of Bokardo is obtained by substitut- 
ing the contradictory of the conclusion for the major premise. 

Reductio per impossibile may be effected in any mood of the 
second figure in the same way as in Baroko ; and in any mood 
of the third figure in the same way as in Bokardo. It was 
specially assigned to these moods in the belief that they could 
not be reduced in any other way. But Baroko may be reduced 
directly (according to the new method of reduction, already ex- 
plained), if we convert the major by the denied consequent; and 
Bokardo, if we convert the minor by the retained necessitant. 

6. Such are the rules of reduction. To promote familiarity 
with them, and with the laws of syllogizing generally, a few 
exercises in connection with some such table of terms as the, 
following, will be found helpful. 







Figure I. 




Moods. 


Major. 


Middle. 


Minor. 


Barbara . . 


. Elastic. 


Gas. 


Oxygen. 


Celarent . 


. Faultless. 


Finite. 


Angel. 


Darii . . . 


. Laudable. 


Virtues. 


Habits. 


Ferio . . 


. Reprehensible. 


Virtues. 
Figure II. 


Habits. 


Cesare . . 


. Material. 


Free-will. 


Spirit. 


Camestres . 


. Color. 


Visible. 


Sound. 


Festino . . 


. Vices. 


Praiseworthy. 


Actions. 


Baroko . . 


. Birds. 


Oviparous. 
Figure III. 


Bipeds. 


Darapti . . 


. Metallic. 


Gilding. 


Shines. 


Disarms . . 


. Laudable. 


Homicides. 


Cruel. 


Datisi . . 


. Cruel. 


Homicides. 


Lawful. 


Felapton . 


. Moral. 


Material. 


Extended. 


Bokardo 


. Wise. 


Men. 


Rational. 


Feriso . . 


. Advantageous. 


Dishonesty. 


Tempting. 



Chap. XXV. ] BED UCTION 


OF SYLLOGISMS. 






Figure IV. 


Moods. 


Major. 




Middle. Minor. 


Bramaiitip 


. Greyhounds. 




Dogs. Quadrupeds 


Dimaris . 


. Virtuous. 




Necessarians. Speculators. 


Camenes 


. Euminant. 




Four-stomached. Carnivore. 


Fesapo . 


. Negroes. 




Hindoos. Colored. 


Fresison 


. Moral Princii 


)le. 


Animal Impulse. Principle of 



289 



Let a syllogism be constructed in every mood of each, figure 
with, the terms given above ; and then let each argument in a 
subordinate mood be reduced to the first figure. In this latter 
work the rules of Hispanus may be employed first ; and then 
that simpler method which has been proposed, and which 
merely converts the major premise in the second figure ; the 
minor, in the third ; and both premises, in the fourth. 

7. After all this, the construction of the unguarded, or con- 
jectural, moods, and their reduction (according to the new 
method) will present no difficulty ; and may be exemplified in 
connection with the following table of terms : 







Figure I. 




Moods 


Major. 


Middle. 


Minor. 


IAI . . 


. Fatal. 


Accidents. 


Railroad Collision 


Ill . . 


. Over- indulged 


Pet. 


Dog. 


OAO. . 


. Fatal. 


Diseases. 


Fever. 


OIO . . 


. . Profitable. 


Speculation. 
Figure II. 


Investment. 


AAI . . 


. Horse. 


Animal. 


Quadruped. 


All . . 


. Serpent. 


Reptile. 


Venomous. 


IAI . . 


. Venomous. 


Reptile. 


Serpent. 


Ill . . 


. Metal. 


Hard. 
Figure III. 


Mineral. 


Ill . . 


. Metal. 


Hard. 


Mineral. 


OIO . . 


. Metal. 


Hard. 
Figure IV. 


Mineral. 


All . . 


. Serpents. 


Reptiles. 


Venomous. 


Ill . . 


. Intelligent. 


Man. 


Unprincipled. 



These unguarded modal syllogisms have hitherto been over- 
looked. But they express a conjectural kind of reasoning 
which is not uncommon. 



290 THE MODALIST. [Chap. XXVI. 



CHAPTER XXVI. 

FALLACIES. 

Paralogisms in Separate Inference. 

1. Our simple and immediate perceptions are reliable. Error arises 
only in connection with tlie complex, and the inferential. Fallacy, para- 
logism, sophism, denned. Truth and falsity are either logical or real. 
2. In correct argument a conclusion really false, shows falsity in the prem- 
ises ; but a conclusion really true may follow from false premises correctly. 
In fallacious reasoning premises and conclusion do not in any way involve 
each other. 3. Eight forms of inference, each of which has its own para- 
logisms. 4. And each of which may be expressed syllogistically.. 5. A 
comprehensive enumeration of fallacies. 6. The hypothetical syllogism 
(and its fallacies) discussed. 7. Disjunctive syllogisms. 8. Relational 
syllogisms. 9. Problematic syllogisms. 10. The paradigmatic syllogism. 
11. Principiative, and inductive, syllogisms. 12. The applicative syllogism. 
13. The Aristotelian, or catenate, syllogism. 

1. Perceptions, absolutely simple and immediate, are exempt 
from error. But, in a complex apprehension, or in a process 
of inference, the mind can suppose some element to be present 
when it is absent, or absent when it is present ; and can wrongly 
connect a consequent with an antecedent. In these ways error 
may arise, in any finite intellect. The liability to error, how- 
ever, is greater in some than in others ; and it is so far unnat- 
ural to a sound intellect that it can be guarded against, and 
often entirely obviated, by care and circumspection. 

An act or process of argument may have the appearance of 
being conclusive, without being really so. In that case, in 
token of its fitness to mislead, it is called a fallacy ; simply 
as a deviation from the laws of right reasoning, it is named a 
paralogism ; and, as employed with the intention to deceive, 
it is termed a sophism. 



Chap. XXVI.] FALLACIES IN SEP ABATE INFERENCE. 291 

The conclusion asserted in a fallacy is often said to be false, 
no matter whether it state truth or not. This signifies merely 
that it is falsely asserted to follow from the premises. In the 

syllogism, 

Good men are sincere ; 

The apostles were sincere ; therefore 

They were good men, 

all the propositions are true; but the conclusion is logically 
false. 

In like manner, that is often called a true conclusion which 
necessarily follows from the premises ; whether it be true in 
itself or not. In this sense the syllogism 

All Orientals speak Arabic ; 

All the Chinese are Orientals ; therefore 

All the Chinese speak Arabic, 

has a true conclusion ; though the proposition in itself is false. 

2. In every correct argument, if nothing be falsely assumed, 
the conclusion must be true in itself, as well as logically. 
Therefore, if a conclusion be logically true, but really false, 
one or other, or both, of the premises must be false. What is 
false can be correctly inferred only from what is false. 

But we cannot say that, if a conclusion has been correctly 
drawn, the premises must be true. A consequent may be 
inferred, not from one antecedent only, but from many; and 
among these may be those purely imaginary, and unreal. We 

might say, 

All stones are moral beings ; 
All men are stones ; therefore 
All men are moral beings ; 

and this syllogizing would be correct. 

In right reasonings, therefore, if the premises be true, the 
conclusion is true, and if the conclusion be false, the premises 
are false, or at least one of them ; but we cannot say that if 
the premises be false, the conclusion is false ; nor that if the 
conclusion be true, the premises are true. On the other hand, 
in fallacious reasoning, there being no true sequence, the con- 
clusion asserted may be either false or true, no matter what 
the character of the premises may be ; and the premises, like- 



292 THE MOBALIST. [Chap. XXVL 

wise, either false or true, no matter of what character the 
conclusion may be. 

3. Fallacies may occur in connection with every form of infer- 
ence; and should be discussed in connection with each separately. 
Especially we must avoid that confusion which attends the 
theory, that there are only two or three species of inference j 
for no confusion is more perplexing than that of a false 
simplification. Logical sequence has a variety of modes, all 
subject to the generic law of reason and consequent, but each 
of which has its own rules, and is affected by fallacy in its 
own way. 

In order to judge wisely respecting sequence, and error in 
sequence, we must distinguish the translative, the disjunctive, 
the relational, the problematic, the paradigmatic, the principi- 
ative, the applicative, and the catenate, inferences. 

4. In each of these modes of sequence, with one or two par- 
tial exceptions, the antecedent is complex, and may be divided 
into two parts ; and so the process may be given a syllogistic 
shape — in other words, may be expressed by two premises 
and a conclusion. For this is what we mean at present by a 
syllogism. All the above-mentioned modes of inference have 
been syllogized, either anciently or in modern times, except, 
perhaps, the problematic, that is, the immediate inference of 
some consequent as probable, or as contingent, or as possible. 
But probable sequence may be analyzed into 

(1) a fact, or antecedent, originating certain chances, — as 
that a ball is to be drawn from a bag in which there are 30 
white and 70 black balls ; 

(2) a determination of the ratio of the chances as being 3 to 
7, or 3 out of 10, or T 3 ¥ , in favor of a white ball ; and 

(3) a conclusion, with the probability of -j%, that a white 
ball will be drawn. Thus we obtain two premises and a con- 
clusion. 

So, in every contingent judgment, there is 

(1) an antecedent fact originating chances ; 

(2) the perception that an appreciable proportion of these 
favor a specific consequent ; and 

(3) the corresponding assertion of that consequent. 



Chap. XXVI.] FALLACIES IN SEPARATE INFERENCE. 293 

Syllogizing after this fashion may not be ordinarily needful 
for the critical understanding of problematic sequence ; but it 
will be found helpful in most cases of the " calculation of 
probability," and in the analysis of certain fallacies. 

The inference of possibility, which is the simplest mode of 
problematic sequence, presents one of the partial exceptions 
mentioned above. It arises when A either is, or contains, a 
condition of B. In the former case we say, 

The being is rational ; therefore 
He may — or may not — be wise. 

Here the antecedent is properly expressed by one premise, or 
one term. But when the antecedent contains the condition, 
we might say, 

(1) Man involves rationality ; 

(2) nationality conditions wisdom ; therefore 

(3) Man may — or may not — be wise. 

This is a syllogism ; indeed, as generalized, it is a conjectural 
catenate syllogism. 

Eelational sequences intuitively and orthologically assert 
the existence of some specific relation or relatum as necessarily 
connected with some antecedent; they are the immediate 
perceptions of the metaphysical and mathematical connections 
of things, and of things as in these connections. We call them 
relational only par eminence; and because they are founded on 
relations which are specific, and not on those which are common, 
or universal. When they have very simple antecedents they 
present a second partial exception to the rule that every mode 
of inference may be given appropriate syllogistic expression ; 
for example, 

There is a body ; therefore 
There is occupied space ; — 

There is a power ; therefore 

There is a substance in which it resides ; — 

There is an action ; therefore 
There is an agent. 

In such cases the antecedents are too simple for analysis. But 



294 THE MOD A LIST. [Chap. XXVI. 

if these simple antecedents be embodied in others more com- 
plex, we can use analysis and say, 

(1) The stone is a body ; 

(2) As such it occupies space ; therefore 

(3) There is occupied space ; — 

and so with every such argument. Here again generalization 
produces a catenate syllogism. Moreover, we have already 
seen (Chap. XXII.) that relational sequences often have com- 
plex antecedents, and that in this case they are naturally stated 
in peculiar syllogisms of their own. For example, 

A is greater than B ; and 

B is greater than C ; therefore 

A is greater than C. 

5. Let us now enumerate the leading modes of fallacy ; and, 
after that, discuss them. 

(1) In simple translative inference, which is expressed by 
the "hypothetical" syllogism, two modes of paralogism are to 
be avoided — that of the denied antecedent, and that of the 
asserted consequent. 

(2) The disjunctive syllogism, which is a complicated mode 
of the translative, is also subject to two modes of error — 
these may be named the omitted alternative, and the false 
contrary. 

(3) In relational inference mistakes occur either through 
some false assumption, or through some confusion respecting a 
premise or a conclusion. 

(4) Fallacies in probable inference arise when the contingent 
is confounded with the necessary, or vice versa; or when the ratio 
of the chances is wrongly computed. In mere possibility there 
may be false assumption of a condition j or of an antecedent as 
containing one. 

(5) Paradigmatization may be erroneous either because of a 
misunderstood precedent, or because of a false comparison. 

(6) Principiation may show either premature interpretation, 
or credulous theory -worship. 

(7) The applicative syllogism may have a false sumption 
(major premise), or a false subsumption (minor premise). 



Chap. XXVI.] FALLACIES IN SEPARATE INFERENCE. 295 

(8) Finally, catenate syllogizing may be defective either in 
the combination of its premises, or in one or more of its sequences 
(or propositions) considered singly. 

6. The hypothetical syllogism is interesting, because its 
peculiar closeness to the fundamental law of all reasoning 
gives to its rules an universal applicability. Any argument 
whatever may be thrown into hypothetical form ; and then we 
immediately see that it is composed of a reason and a conse- 
quent. Some confine the hypothetical syllogism to apodeictic 
sequence, but there is no ground for any such limitation. 

The first rule of inference is that if the antecedent be asserted 
the consequent may be asserted, but that if it be denied, nothing 
follows. Therefore to deny the antecedent and to claim a 
consequence, either positive or negative, is a paralogism. Exact 
apodeictic sequences, such as are based on definitions and 
mathematical conversions, form an exception to this rule ; in 
these we either assert or deny either antecedent or consequent, 
and in every case have a consequence. But this exception 
does not destroy the rule. 

The second rule of inference is that, in any apodeictic se- 
quence, the denied consequent is followed by the denied antecedent. 
But, with the exception mentioned above, to assert the conse- 
quent, in order to produce an apodeictic converse, is fallacious. 
Because " iron is fusible," we cannot say " what is fusible is 
iron." The Greeks termed this error the varepov irporepov, since 
it puts that first which should be last. 

But the asserted consequent is not fallacious if we infer 
only contingency, and say "what is fusible may be iron." 

7. The " omitted alternative " and the " false contrary " are 
the fallacies of disjunctive reasoning : they can be easily un- 
derstood if we consider, first, the modes of disjunctive asser- 
tion, and then the modes of disjunctive inference. 

Disjunctive assertion arises when an antecedent supports a 
plurality of alternative consequents ; and it may be either strong 
or weak. In strong disjunction the alternatives are contraries 
of one another ; as when Ave say, " The season is either spring, 
summer, autumn, or winter." In weak disjunction the alterna- 
tives are compossible ; they may exist together, though they 



296 THE MODALIST. [Chap. XXVI. 

cannot all be non-existent at once. Thus, in saying above, 
" Catenate syllogizing may be defective either in the combina- 
tion of premises or in one or more of its sequences considered 
separately," we do not mean that it may not have both these 
faults at the same time. To say, " The man is either a fool 
or a knave or a fanatic," means that he has one of these 
•characters at least, not that he has one only. 

Disjunctive inference, also, has two modes, the positive, or 
the tollendo ponens; and the negative, or the ponendo tollens 
(Chap. XVIII.). The former of these employs for "major" 
premise either a strong or a weak disjunction, indifferently. 
On denying all the alternatives but one, we assert that one 
absolutely; or, on denying several conjointly, we can assert the 
rest disjunctively. Evidently, in either case, every alternative 
must be taken into consideration. Our only ground of positive 
assertion respecting one or several alternatives, is that all the 
rest have fallen out of the race. Therefore the "omitted 
alternative " is a fatal defect in any case of tollendo ponens. 

On the other hand, in the ponendo tollens, we assert one 
contrary alternative, and then deny conjointly as many of the 
rest as we please ; there is no need that we should think of 
all. But we must now guard against the paralogism of the 
" false contrary." The ponendo tollens is valid only with true 
contraries. We cannot say that, because the man is a fool, 
therefore he is not a knave or a fanatic. 

Such argumentation, indeed, can be rendered valid if the 
alternatives be conceived as exclusive of one another, and 
another alternative be added for the possible union of two or 
more of the single alternatives. If the man be either simply 
a knave or a fool or a fanatic, or more than one of these at 
once, then, if one of these things be true, each of the rest is 
false. This, however, so alters the reasoning that it is no 
longer the same argument. 



8. Relational inferences — even when they have complex 
antecedents and may be analytically syllogized — are extremely 
simple, and not in themselves liable to error. Fallacies in 






uJL \<\-i* 



Chap. XXVI.] FALLACIES IN SEPARATE INFERENCE. 297 

metaphysical and mathematical reasonings arise from primary 
misapprehensions, and from confusions of thought; rather than 
from any difficulty in ontological sequence itself. For instance, 
the metaphysical doctrine held by some that there are activi- 
ties without an agent, and powers without a substance, springs 
partly from the unfounded prepossession that our faculties of 
immediate cognition perceive only " phenomena," and not also 
those permanent factors by which actions and changes are 
produced ; and partly from a confusion which takes things to 
be separable because they can be separately conceived of and 
mentioned. So also mathematical error originates in concealed 
confusion and assumption; not through any. mistake in axio- 
matic sequence. 

The fraction when developed, gives the endless series 

1 — x 

1 -f- # -f- ar -f- cc 3 -h • • • -h x°. Substituting the value 3 for x in 
the fraction and in the series, and placing the results in equa- 
tion, we have — |-=l-|-3-|-9+ 27 + 81 + •••, and so on in- 
definitely. Thus a quantity less than nothing, or rather a 
definite subtractive quantity, appears to be equal to an addi- 
tive quantity indefinitely large. 

The paralogism of this lies in failing to note that, no matter 
to what extent the series may be developed, there will always 
be a remainder with which the series must be terminated. If 
we stop dividing when x s has been obtained, there will be a 

remainder requiring to be added to the quotient, i.e. to 

1 — x 

x 5 

the series. If we stop with x A , must be added. In other 

1 — x 

words, if we stop with 27, the quantity — *£- will be required 
to complete the series, or if we stop with 81, the quantity 
— ^3- will be required. But, combining either of these with 
the sum of the preceding terms, we obtain — J = — | ; and all 
contradiction disappears. 

That men do not err in their immediate ontological intui- 
tions, but only through some wrong apprehension of premises, 
or through some confusion or commutation of ideas, seems to 
be the doctrine of Aristotle, when he contrasts S6£a, which may 
be erroneous, with eTrto-r^, which is "always true" (" Analyt. 



298 THE MODALIST. [Chap. XXVI. 

Post.," II. 19). It is also the basis of the paradox of the Latin 
poet, 

"Nam neque decipitur ratio, nee decipit unquam." 

9. In problematic sequence, fallacies in possibility do not 
call for separate consideration. The inference of the possible, 
when it is onthological, may be classed with those relational 
inferences of which we have been speaking, and, when it is 
homological, is subject to the accidents of homologic syllo- 
gizing. But probability, and contingency, which is indetermi- 
nate probability, require a specific discussion. 

Probable inference has this in common with the disjunctive, 
that in both we conceive of the contingent and conflictive con- 
sequents of one antecedent ; in other respects these modes of 
sequence differ widely. Till comparatively recent times prob- 
ability has been treated as either not admitting or not needing 
analysis ; and has not been distinguished from contingency. 
Even now, though understood by philosophers and mathema- 
ticians, it has scarcely secured a place in " formal " logic. But 
it has a distinct nature of its own; and, as we have seen, may 
be expressed by a peculiar syllogism. In this the first premise 
sets forth an antecedent which supports a limited number of 
chances, or possible individual consequents ; the second deter- 
mines a ratio between the chances for some specific consequent 
and the whole number of chances ; and the conclusion asserts 
that consequent with the corresponding degree of likelihood. 

Such being the case, two general forms of error are notice- 
able. We may either mistake the character of the antecedent, 
and suppose that to be necessary which is only contingent; or we 
may miscalculate the ratio of the chances. 

The substitution of the necessary (or the impossible) for 
the contingent, is the fault of those who either believe too 
easily that every exigency has been provided for, or who give 
way to despair while there is yet ground for hope. 

This, also, is the defect of that philosophy which makes no 
distinction between extreme probability and absolute necessity. 
What is very highly probable is sometimes called "morally 
certain"; yet the opposite of it is entirely possible, and, under 



Chap. XXVI.] FALLACIES IN SEPARATE INFERENCE. 289 

peculiar conditions, may become probable. But the opposite 
of the necessary is impossible. 

Moreover, absolute impossibility does not arise from con- 
nection with any instituted order of things ; for that order 
may be changed or interrupted ; but from conniction with the 
laws of being, or the necessary nature of things. Unprejudiced 
consideration should enable one to say whether an alleged fact 
or event be impossible in this way or not. 

When an event is seen not to be impossible, its probability 
cannot be properly determined, unless the circumstances of the 
case be fully considered. Probability varies wonderfully with 
variations in the antecedent. ]STor is it sufficient to note that 
a thing has happened often in a certain case, or, for some other 
reason, has many chances in its favor ; we must estimate the 
ratio of its chances in connection with the definitely ascer- 
tained antecedent. To this end a power of close, accurate, 
and dispassionate consideration must be developed ; otherwise 
one's judgments in contingency will be without weight, and 
little more than plausible conjectures. Moreover, in the math- 
ematical compounding of probabilities, much care is needed 
if we would avoid intellectual displacements (" The Human 
Mind," Chap. XXIV.). 

10. While Aristotle teaches that every inferential process 
may be stated syllogistically, he distinguishes paradigmatic and 
inductive syllogisms from those in which ive reason from general, 
or universal, statements. He shows that they express modes of 
inference quite different from those of the ordinary categorical 
syllogism. ("Analyt. Prior.," II. 25, 26). According to him, 
arguments from example {irapahay^aTa) are not based on the re- 
lation of the universal to the particular (as ordinary syllogisms 
are), nor on that of the particular to the universal (as induc- 
tions are) ; but on that of the particular, or specific, to the 
particular, or specific. In short, we reason from one indi- 
vidual, or specific, sequence to another, when the one, but not 
the other, of these has been already ascertained. 

Aristotle, indeed, teaches that one specific sequence is infer- 
able from another because a general law can be discerned in, 
and obtained from, a given precedent, or from several given 



300 THE MODALIST. [Chap. XXVI. 

precedents ; but this is entirely consistent with his doctrine, 
that the reasoning is from the specific, or the individual, and 
not from the general. Tor not the general principle, but only 
the specific case, is given. 

Moreover, while his words favor the view that inference 
from example operates through (though not from) the general, 
he probably would allow that the generalization might be 
dispensed with, provided there be that exact understanding of 
the prior sequence upon which a true generalization (or prin- 
cipiation) might be made. Locke distinctly teaches the doc- 
trine that a second specific sequence may be directly inferred 
from a first ; provided the antecedent of the second agree with 
the antecedent of the first in those respects which are perceived 
to be essential. 

Such being the case, two modes of error are possible in 
paradigmatic syllogizing. Either the prior sequence, which 
might be called the major premise, may be misunderstood, so 
that either the antecedent or the consequent of it is wrongly 
conceived; or, if the prior sequence be correctly ascertained, 
the minor premise may falsely assert that the new antecedent 
is essentially similar to the old. The best plan to avoid error 
in doubtful cases, is to exact a definite law from the prior 
sequence by principiation ; and then to test this law, and reason 
from it. The thoughtful mind naturally adopts this method. 
And this shows how closely the paradigmatic and the applica- 
tive syllogisms are related to each other; and why the former 
has been overlooked and neglected by logicians. 

11. The inductive syllogism, yet more than the paradigma- 
tic, is recognized by Aristotle. He says ("Prior. Analyt.," II. 
25) that when there is a middle term we syllogize through 
that (Sia tov /xeaov), but when there is no middle term, through 
induction (St eVaycoy^s). He even opposes "induction" to 
" syllogism," — that is, to applicative and catenate inference ; 
in both of which we infer through a middle term. 

According to Aristotle all first principles (Trpwrai apx<u) are 
obtained by induction. In the last chapter of his "Posterior 
Analytics," he begins a discussion concerning first principles 
by speaking of that power of perception whereby we obtain the 



Chap. XXVI. ] FALLACIES IN SEPARATE INFERENCE. 301 

knowledge of individual facts and truths, — Bwafuv o-vp.<f>vrov 
KpLTiKrjv, yv KaXovatv ouaOrjcnv ; — and he finishes the discussion 
by saying that first principles are obtained by induction from 
this perception ; — Srjkov S?) otl rj/juv ra irpwTa lirayoiyrj yvwpt^uv 
ava.yKa.iov ' koX yap kol aicr0r)O~i<s ovtu) to KaOoXov £p.iroiu. In this 
passage "induction" has the broad sense of " principiation." 
The doctrine thus taught is very acceptable to those who now 
call themselves " Perceptionalists." 

Further, it is to be allowed that gathering and collating are 
not absolutely essential to induction. Often a natural law has 
been ascertained by one demonstrative experiment ; while nec- 
essary, or ontological, sequences, on account of their forceful 
simplicity, may be principiated instantly from a single illus- 
tration. It can only be said that the inductive syllogism 
ordinarily reaches its conclusion through the analytic compar- 
ison of a collection of instances ; because cosmological se- 
quences — or the instituted laws of Nature — cannot, as a rule, 
be exactly determined in any other way. 

Therefore, in the first, or major, premise, the different indi- 
vidual antecedents are set forth as having, by reason of some 
common nature, the same consequent : 

These oaks, beeches, elms, maples, etc., have roots. 

The second, or minor, premise states what this common nature 

is; 

These oaks, beeches, elms, maples, etc., are trees, 

whereupon the conclusion attaches the consequent to the 
nature, or to the whole logical class as having that nature ; 

Trees have roots. 

This conclusion is certain when the premises justify an 
universal rule ; probable, if they warrant only a rule with 
exceptions. Probability is not necessarily, or inseparably, 
connected with induction ; and the homological law, on which 
all principiation rests, is, in itself, ontological and apodeictic. 

Induction, like probability, has many specific rules and 
modes of fallacy, which cannot be considered in a general logic. 
But two comprehensive forms of paralogism may be mentioned. 



302 THE MODALIST. [Chap. XXVI. 

The first of these is the premature interpretation of the indi- 
vidual sequences; and this may affect either premise. When we 
say, in the major, that a, b, c, d, e, etc., have each the conse- 
quent C, we must be sure that there is a real consequence in 
each case ; and not a mere accidental connection. To assume 
a sequence simply because one thing may have happened 
sometimes in conjunction with another is to substitute chance 
for law. " Simple enumeration " is only the beginning of the 
inductive process ; and even this enumeration is valueless if it 
be one-sided, ignoring either negative or affirmative instances. 
How worthless are the cases with which quacks advertise their 
nostrums, and on which the superstitious base their expecta- 
tions of good or of evil ! Scientific teachings, too, occasionally 
are affected with hasty or superficial interpretations. When- 
ever the operation of causes is complex — for example, in the 
problems of sociology — only wise discrimination can say what 
are, and what are not, the consequences of given antecedents. 
In such cases, abandoning immediate principiation, we should 
separately analyze and ascertain the operation of each factor* 
In this way we may at last reach a satisfactory conclusion. 

The important part of induction lies in exactly determining 
and understanding the individual sequences of the major 
premise ; after this, the antecedent of the conclusion, to be 
asserted as predicate of the second premise, and which com- 
pletes the interpretation, is obtained by defining that common 
character which belongs to the individual antecedents ; and 
gives to each its efficacy. This also calls for care and 
deliberation. 

Errors of interpretation are often re-inforced by a strange 
credulity with which plausible theories are received. Never con- 
tent with ignorance, even when knowledge may be difficult or 
impossible, men form conjectures about all things. This habit 
is not irrational; nor are conjectures to be despised, if they 
be not visionary. Yet it has constantly happened in the his- 
tory of science that doctrines, which have been at best merely 
conceivable hypotheses, have been advocated and taught as if 
they were established truths. This mistake has been committed 
by men of ability, who have been wanting in maturity of judg- 



Chap. XXVI.] FALLACIES IN SEPARATE INFERENCE. 303 

merit, but who wish to rank among " advanced thinkers " ; and 
even sometimes by distinguished observers of Nature who have 
not, either theoretically or practically, mastered the laws and 
limitations of inductive reasoning. 

12. The applicative syllogism, because of its simplicity, is 
comparatively free from liability to error ; but it may become 
fallacious either through a, false "sumption" or major premise, 
or through a, false subsumption, or minor premise. The former 
results from some prior fallacy, or misconception, or misstate- 
ment ; while a deceptive subsumption, in a similar way, either 
falsely ascribes some character to a subject, or ascribes a char- 
acter which does not make that subject agree with the subject 
of the sumption. For, in every correct applicative syllogism, 
the sumption sets forth a general truth ; and the subsumption 
an individual or singular subject, as having the nature of the 
subject of the sumption; whereupon, in the conclusion, the 
predicate of the sumption is asserted of the individual subject. 

13. We have now considered the fallacies of unconnected, 
or separate, as distinguished from those of connected, or cate- 
nate, inference. These latter remain to be discussed. They 
are those immediately related to the Aristotelian syllogism; 
and which, therefore, have chiefly engaged the attention of 
logicians. 



304 THE MODALIST. [Chap. XXVII. 



CHAPTER XXVII. 

FALLACIES IN CATENATE INFERENCE. 

1. Catenational fallacies are of two classes : (a) the interior, (6) the 
exterior; commonly called the "formal," and the "material." 2. They 
may be subdivided into seven classes. 3. The "four-terms," and the 
"ambiguous middle." 4. The fallacy of "accident" proceeds " a dicto 
secundum quid" either " ad dictum simpliciter " or " ad dictum secundum 
alterum quid" ; and maybe interpreted in either of two ways. 5. The 
spurious fallacy of accident is merely a case of equivocation. 6. The fal- 
lacy of "negative-premises" has two modes: (a) "the uncontradicted- 
middle," and (&) "the unasserted-middle." 7. "Illicit-process of the 
major," relates to negative syllogisms. 8. " Illicit process of the minor," 
relates to contingent syllogisms. 9. The "undistributed-middle," is 
(a) fatal to the operation of the " separating-consequents," (&) weakening 
to that of the " consequent-consequent." 10. Is to be avoided in the first 
figure by an apodeictic major ; but in the third figure an apodeictic minor 
suffices. Summary of doctrine respecting this fallacy. 11. The fallacy of 
two contingent premises is essentially the same with the "undistributed- 
middle. ' ' 12. An apodeictic conclusion cannot follow a contingent prem- 
ise ; hence universal affirmatives are naturally proved in the first figure 
only. 

1. Most logical writers take the catenate syllogism, and that, 
too, in its dogmatic form, as the fundamental type of reason- 
ing; hence they discuss fallacies in connection with it, and 
as deviations from its laws. This course fails to consider 
things according to their true differences. To understand 
fallacies we must separate the catenate from the applicative 
inference, and yet more from the principiative, the translative, 
and the other modes. Every form of inference has laws of 
its own, which may be violated. 

Paralogisms in catenate syllogizing are of two general classes. 
Those of the first class arise from a wrong combination of 
premises, and are such as peculiarly affect the catenation of 



Chap. XXVII.] FALLACIES IN CATENATE INFERENCE. 305 

sequences; those of the second class flow from the falsity 
of separate sequences, and are traceable to causes not specially 
connected with catenate syllogizing. 

With reference to their origin, fallacies of the first descrip- 
tion might be named interior catenational fallacies; and those 
of the second, exterior catenational fallacies. The former result 
exclusively from the want of a proper catenation between 
terms, so that logical sequence fails; the latter wrongly as- 
sume terms in a premise, or wrongly substitute terms in the 
conclusion. In each of these last-mentioned cases there may 
be true catenation : but in the one the conclusion rests on 
unwarranted assumption ; and in the other the conclusion sup- 
ported by the premises, is falsely identified with that which 
ought to have been proved. 

These interior and exterior fallacies ordinarily receive the 
designations "formal" and "material"; the one being supposed 
to relate exclusively to the nature of logical sequence, and the 
other to the nature of specific antecedents and consequents. 
This distinction is inaccurate : both modes of paralogism are 
directly related to the nature of sequence ; and in either mode 
any particular fallacy must be explained with reference to the 
matter considered. The one, indeed, brings logical connection 
into prominence, and the other, the character of the things 
reasoned about ; but neither is exclusively " formal," or exclu- 
sively "material." 

2. Interior catenational fallacies may be treated under the 
five following heads : 

(1) The fallacy of four terms ; and of the ambiguous term. 

(2) The fallacy of negative premises; and of an affirmative 
conclusion with either premise negative. 

(3) The illicit process of the major premise ; and the illicit 
process of the minor. 

(4) The undistributed-middle : first, as in syllogisms of the 
consequent-consequent ; and secondly, as in syllogisms of the 
separating-consequents. 

(5) The fallacy of a guarded conclusion with both prem- 
ises particular; and of an apodeictic conclusion with either 
premise particular. 



306 THE MOBALIST. [Chap. XXVII. 

Exterior catenational fallacies may be treated under two 
general heads : 

(1) The petitio principii; in which either premise is assumed 
without warrant, and 

(2) The ignoratio elenchi; in which the true point at issue 
is ignored, and an irrelevant conclusion proved instead. 

3. Adopting the order of the above divisions, we begin with 
the fallacy of four terms (quattnor termini). More exactly 
speaking, this is the fallacy of using more than three terms ; 
it is a violation of the rule that catenation requires three terms 
and admits three only. Other modes of inference employ four 
terms or more. Should we say, 

A is equal to B ; 

B is equal to C ; therefore 

A is equal to C, 

we would use four terms, A, B, equal to B, and equal to G. 
This, however, is not a catenation of sequences, but a single 
sequence which has for subject, or antecedent, "A, being equal 
to B. which is equal to (7," and for predicate, or consequent, 
"equal to CP So, also, paradigmatic and inductive inferences 
use more than three terms ; and may use even many, if each 
example, or instance, be counted as having an antecedent and 
consequent of its own. 

On the contrary, catenation with more than three terms is so 
evidently fallacious that it is never attempted except under 
some carelessness and confusion. In saying, 

A wicked man desires happiness ; 

The only road to happiness is virtue ; therefore 

A wicked man pursues virtue, 

five terms are used. Yet the argument might be taken as a 
syllogism of three terms. 

In most cases the fallacy of four terms is concealed under 
some ambiguity, one of three terms being employed in two 
senses, and serving really as two terms. This occurs with the 
middle term more frequently than with either of the others ; 
and hence this form of the fallacy is commonly known as the 
" ambiguous middle." But sometimes, instead of the middle 



Chap. XXVII.] FALLACIES IN CATENATE INFERENCE. 307 

term having different meanings in the premises, the major, or 
the minor, term, has one meaning in its premise and another 
in the conclusion. 

Fallacies of ambiguity have received various names accord- 
ing to their origin. When the paralogism arises because the 
same word or phrase has two significations, and is therefore 
" equivocal," it is called the fallacy of equivocation. Thus one 
might argue that since " criminal actions " should be punished, 
prosecutions for theft should be punished; because they are 
" criminal actions." Again, the paralogism based on an am- 
biguous grammatical construction, is styled the sophism of 
amphibology ; for a sentence containing such a construction is 
termed amphibolous. Thus, 

Twice two and three is seven ; 

But ten is twice two and three ; therefore 

Ten is seven. 

Closely related to such fallacies are those of Division and of 
Composition. These arise from using an universal expression 
collectively in one premise, and distributively in the other. 
In the following we proceed from division to composition, and 
commit the fallacy of composition, 

All the angles of the triangle are less than two right angles ; 
A, B and C are the angles of the triangle ; therefore 
They are (collectively) less than two right angles. 

On the other hand it would be & fallacy of division to say, 

All the angles of the triangle are equal to two right angles ; 
A is an angle of the triangle ; therefore 
It is equal to two right angles. 

The fallacy of " accent " arises when an improper antithesis 
is attached mentally to some part of a sentence, and expressed 
by emphasis. " Love the brethren " might mean " the brethren, 
but not strangers " ; and so one could say, " He is not my 
brother ; I need not love him." 

The fallacy of the figure of speech proceeds from the figura- 
tive signification of a term to the literal ; or from the literal, 
to the figurative. If our Saviour's words, "This is my body," 



308 THE MODALIST. [Chap. XXVII. 

be figurative, the argument from it in favor of the " real pres- 
ence " in the Eucharist is illogical. 

4. Lastly, among errors of ambiguity, we name the "fallacy 
of accident " ; of which there are two forms, the genuine and the 
spurious. The former arises when we reason from a nature 
with an accidental addition, as if it were a nature viewed sim- 
ply, or per se — that is, from what is true specifically, as if it 
were true universally. In the fallacy of accident we proceed 
" a dicto secundum quid " either " ad dictum simpliciter " or " ad 
dictum secundum alterum quid." For this mode of paralogism 
assumes that what is true of a species is necessarily true of 
the genus, or of another species. Should we say, 

What destroys health should not be used ; 
Intoxicants destroy health ; therefore 
No intoxicants should be used, 

this would be a case of " a dicto secundum quid ad dictum sim- 
pliciter" ; because the minor premise does not mean that intox- 
icants, as such and always, ruin health. But should we say, 

To take life is not sinful ; 

Murder is the taking of life ; therefore 

Murder is not sinful, 

the " taking of life " would be spoken " secundum quid " in the 
major premise, and " secundum alterum quid " in the minor. 
Only certain modes of killing are not sinful ; and only certain 
other modes are murder. 

According to the foregoing explanation, the fallacy " a dicto 
secundum quid " (the genuine fallacy of accident), is an error 
of ambiguity ; but it may also be interpreted as an error in 
distribution, or modality. The thought of the argument being 
only partially expressed, we may make the fallacious premise 
either an universal assertion regarding an unnamed and under- 
stood species, or a contingent assertion regarding the genus. 
To say, " the taking of life with just cause is not sinful " is spe- 
cific and apodeictic ; to say " the taking of life is not necessarily 
sinful " is generic and contingent. Completing our thought in 
the former way, without expressing the completion, the fallacy 
is an ambiguous middle ; completing it in the other way, it is a 



Chap. XXVII. ] FALLACIES IN CATENATE INFERENCE. 309 

case of " undistributed middle " ; a fallacy of which we shall 
speak presently. 

The easier mode of refuting the error seems to be to refer 
it to an ambiguity. The sophism, 

What grows on sheep is raw wool ; 

Those who wear woollens wear what grows on sheep ; therefore 

Those who wear woollens wear raw wool, 

is best refuted by showing the double meaning of the middle 
term "what grows on sheep." In one premise this signifies 
" what grows on sheep in its primitive condition " ; but in the 
other, "what grows on sheep in its manufactured condition." 
We might, however, adopt the modal interpretation, and deny 
that "what grows on sheep is (always) raw wool"; in which 
case the fallacy would be one of distribution. 

5. The spurious fallacy of accident does not admit of a 
double treatment. It is founded on that metonymy whereby 
the same term indicates — not a genus and a species — but the 
whole, and a part, of a nature. Should we say, in Darapti, 

Man is mortal ; 

Man is a rational spirit ; therefore 

A rational spirit is mortal, 

the term "man," in the major premise, signifies the whole 
composite being, but in the minor, only a part of that being. 
This paralogism is said to proceed " a dicto simpliciter" (" man" 
in the major) ad dictum secundum quid ("man" in the minor). 
But erroneously ; for we do not proceed from the genus to the 
species, but from the composite whole to its component part. 
To proceed from the generic to the specific is not fallacious. 
Then, should we invert the order of the premises, and infer 

What is mortal is a rational spirit ; 

this also would be an ambiguous middle, not a true fallacy of 
accident. 

In addition to the paralogisms just mentioned, certain others 
have been improperly identified with those of accident. They 
are reasonings concerning individuals, or singulars, as such ; 
and therefore cannot be said to proceed from the specific to 



310 THE MOBALIST. [Chap. XXVII. 

the generic or to the specific. Yet they are closely related to 
the genuine fallacies of accident, because they use terms with 
unexpressed additions. In the relational syllogism, 

The meat we eat to-day was bought yesterday ; 
But that bought yesterday was raw meat ; therefore 
The meat we are eating is raw meat, 

the middle term, "that bought yesterday," is ambiguous by 
reason of two additions. But since these are not the accidents 
of a general essence, the fallacy is not one in catenate syllo- 
gizing. It is an erroneous inference in identity. 

6. The second general mode of eaten ational paralogism is 
that connected with negative premises ; and it has two forms. 
Tor to draw any conclusion from two negative premises, and to 
infer an affirmative conclusion if either premise be negative, are 
direct violations of those principles which govern all catenate 
syllogizing. The law of the consequent-consequent requires the 
minor premise to be affirmative ; and the law of the separating- 
consequents, that one premise, no matter which, be affirmative ; 
neither admit a conclusion if both premises be negative. 

Then, also, the separating-consequents, which has always one 
premise negative, has always a negative conclusion ; while the 
consequent-consequent has always a negative conclusion if the 
major premise be negative. Therefore, with either law, a 
negative premise necessitates a negative conclusion. 

In a case of the separating-consequents, the fallacy of two 
negative premises might be specifically known as " the uncon- 
tradicted-middle" ; because, in this mode of reasoning, one 
premise must assert, and the other deny, the same consequent 
term. But with the consequent-consequent, the fallacy takes 
the form of "the unasserted-middle " ; because, in this mode of 
syllogizing, the middle term, which is assumed as antecedent 
of the major premise, must be asserted as consequent of the 
minor. 

Here, however, we must remember that, with the consequent- 
consequent, if the antecedent of the major premise be negative, 
the minor premise must be negative; and can be affirmative 
only in the sense that it asserts, as its own consequent, the 



Chap. XXVII.] FALLACIES OF CATENATE INFERENCE. 311 

antecedent of the major. In such a case a negative minor 
premise may be followed by an affirmative conclusion; and also 
two negative premises, by a negative conclusion. We can say, 

One who is not helpless should he hopeful ; 

He who is sound in mind and body is not helpless ; therefore 

He should be hopeful. 

And also, 

One who is not helpless should not be despondent ; 

He who has mental and bodily health is not helpless ; therefore 

He should not be despondent. 

7. We now come to those modes of paralogism, in each of 
which a term is improperly used with a distributive, or neces- 
sitant, force. These are the illicit process of the major, the 
illicit process of the minor, and the undistributed middle. 

In the first of these the major term is distributed in the 
conclusion, Avhen it has not been distributed in its premise. 
Such a process is illegitimate; because it puts more into the 
conclusion than the premises warrant. A weaker conclusion 
than can be maintained is not unlawful; but a stronger con- 
clusion is. 

Affirmative sequence, in general, — and therefore an affirma- 
tive conclusion — does not call for a distributed predicate. 
Hence, the major term need not be distributed in the premise 
of an affirmative syllogism. But negative sequence — and 
therefore a negative conclusion — does distribute its predicate 
(Chap. XX.); consequently the major term must be distributed 
in the premise of every negative syllogism. To say, 

Motion is visible ; 

Sound is not visible ; therefore 

Sound is not motion ; 

is entirely inconclusive unless we mean that cdl motion is 
visible. Hence, in negative syllogisms of the second and of 
the fourth figure, the major premise must be universal ; for, 
in these figures, the major term is subject of that premise. 

But in negative syllogisms of the first and of the third figure, 
the major term is predicate of the premise. In such syllogisms, 



312 THE MODALIST. [Chap. XXVII. 

therefore, the major premise need not be universal in order 
to avoid the illicit process ; but it must be negative ; for only 
negative assertion distributes the predicate. Hence, the mood 
Bokardo is lawful; and such conjectural syllogisms in the first 
and third figures, as the following : 

Some hard things are not metals ; 
f Some hard things are minerals (3d fig. ) , or 
I Some minerals are hard things (1st fig.) ; therefore 

A mineral may not be a metal. 

8. The illicit process of the minor distributes the minor 
term in the conclusion, when it has not been distributed in the 
premise. This paralogism is less violent than the illicit process 
of the major. The latter syllogizes when no inference at all is 
warranted ; illicit process of the minor concludes apodeictically 
when only a contingent conclusion can be justified. 

This fallacy will scarcely deceive thoughtful persons, unless 
it should be in the fourth figure. But should we say, 

No Hindoos are negroes ; 

All negroes are blacks ; therefore 

No blacks are Hindoos, 

there would be an illicit process of the minor. The term 
"black" has greater modal force in the conclusion than it has 
in the premise. The proper conclusion would be, 

Some blacks are not Hindoos. 

9. The " undistributed-middle " occurs when the middle 
term is undistributed in both premises ; but not if it be dis- 
tributed in either. While common to all modes of catenate 
inference, it does not affect all alike ; but is a fallacy which 
has two degrees, a stronger and a weaker. 

In the first place, a distributed-middle is necessary to any 
conclusion whatever by the separating-consequents. This princi- 
ple requires the middle term to be predicate of both premises ; 
and one of the premises to be negative. Therefore, the middle 
term must be distributed, as predicate of the negative premise ; 
hence, a distributed-middle is indispensable in every negative 
syllogism of the second figure. 



Chap. XXVII.] FALLACIES OF CATENATE INFERENCE. 313 

This is true, also, of negative syllogisms in the fourth fig- 
ure. For these immediately fall into the second figure, on the 
conversion of the minor premise ; and may be interpreted as 
really governed by the separating-consequents. To say, in 
Fresison, 

No moral principle is an animal impulse ; 

Some animal impulses are principles of action ; therefore 

Some principles of action are not moral principles, 

is essentially an argument in Festino ; and would be wholly 
inconclusive without the distribution of " animal impulse." 

The relation of the undistributed-middle to negative syllo- 
gisms in the fourth figure, may be stated, also, from a more 
radical point of view. In the ultimate analysis these syllo- 
gisms involve the mental conversion of both premises ; one of 
which must be negative. But this involves a distributed- 
middle. For a negative premise, to be convertible, must be 
universal and distribute both terms, one of these being the 
middle term. 

What distinguishes negative syllogisms in the second and 
fourth figures from all others, is that they depend on the 
principle of conversional contradiction ; which is, " contradict 
an apodeictic consequent, and you may deny the antecedent." 
In the second figure the minor premise contradicts the conse- 
quent of the major; and thereupon the conclusion denies the 
antecedent of the major. In the fourth this same process 
takes place, if we mentally convert the minor premise only ; 
but if we convert both premises, and appeal directly to that 
principle in which all syllogizing originates, we must then use 
the " denied-consequent " in converting the negative premise, 
whichever that may be. In either case conversional contra- 
diction is involved ; and in either this requires a distributed- 
middle. For if we reduce to the second figure, then, according 
to the law of that figure, the middle term will be distributed 
as predicate of the negative premise ; while reduction to the 
first figure by converting both premises is conditioned on the 
universal negative premise ; in which the middle term is dis- 
tributed either as subject or as predicate. This absolute need 



314 THE MODALIST. [Chap. XXVII. 

of a distributed middle affects only those syllogisms which, 
depend on conversional contradiction. 

The second, and weaker, form of the " undistributed middle " 
pertains to syllogisms of the first and of the third figure, and 
to the affirmative moods of the fourth figure — in short, to all 
syllogisms which are governed by the consequent-consequent 
alone or with some simple conversional addition. In such 
reasonings the undistributed-middle merely renders the con- 
clusion unguarded, or conjectural. It is a paralogism only 
when employed to prove a guarded conclusion j or any conclu- 
sion that can be expressed dogmatically. 

Distribution of the middle does not of itself ensure a guarded 
conclusion; in any syllogism whatever, if either premise be 
unguarded, the conclusion will be unguarded. But this'second 
mode of the undistributed-middle assumes that both premises 
are guarded ; and is the attempt to reach a guarded conclusion 
from two guarded premises, without a distribution of the 
middle term. Moreover, as there is a sense in which the 
stronger mode of the error belongs to reasonings by the sepa- 
rating-consequents, so there is a sense in which this weaker 
mode is confined to syllogisms of the consequent-consequent. 
Tor all syllogizing may be said to take place on one or other 
of these two principles. 

10. To avoid this fallacy in the first figure, an apodeictic 
major is necessary. The middle term, as predicate of an af- 
firmative proposition, not being distributed in the minor prem- 
ise, it must be distributed, if at all, as subject of the major. 
To say, 

Some virtues are laudable ; 

Some habits are virtues ; therefore 

A habit may be laudable, 

yields a correct unguarded conclusion ; but we must say, 

All virtues are laudable ; 

Some habits are virtues ; therefore 

Some habits are laudable, 

if we would have a guarded conclusion. 



Chap. XXVII.] FALLACIES OF CATENATE INFERENCE. 315 

The reason for this is that if A (habit) be followed in any 
mode by B (virtue), and B necessarily by C (laudable), then 
A is followed in the same mode by C as by B. On the con- 
trary, if A be followed in some mode by B, but B only contin- 
gently by C, it may turn out, notwithstanding a justifiable 
conjecture, that A never is, and never can be, followed by C. 
In other words, without distribution of B the conclusion can- 
not be guarded against impossibility. 

Here, however, it is to be remembered that a guarded con- 
clusion can be reached in a peculiar way, if the middle term 
be distributed in the minor premise, even while that term may 
be undistributed in the major. We can say, 

Some heroes are godlike ; 

Some men are all the heroes ; therefore 

Some men are godlike. 

For if C (godlike) in some way follow B (hero), and B neces- 
sitate A (man), then C must follow A as it does B. But, ex 
hypothesij C follows B with a guarded contingency ; therefore 
the conclusion is guarded. 

This form of reasoning, nevertheless, though logically con- 
clusive, is properly excluded from the first figure; because we 
do not naturally use a contingent antecedent with a necessi- 
tating consequent, but always put the necessitant first; even 
when some mental conversion must follow, in our syllogistic 
use of the assertion. We do not say, " Some men are all the 
heroes," but, "All heroes are men." Hence we reason in the 
third figure, instead of the first, and say, 

Some heroes are godlike ; 
All heroes are men ; therefore 
Some men are godlike. 

Clearly in this case the third figure is really a modification 
of the first; and the chief function of its affirmative minor 
premise is to distribute the middle term, when it has not been 
distributed in the major. And this is equally true respecting 
the positive moods of the fourth figure; each of which can 
distribute the middle term only as the subject of the minor 
premise. 



316 THE M0DAL18T. [Chap. XXVII. 

The law respecting the distribution of the middle term may 
be summed up as follows : All catenate syllogisms are divisi- 
ble into two classes j those which depend on conversional 
contradiction, and are essentially syllogisms of the separating- 
consequents ; and those in which that principle is not employed, 
and which are essentially syllogisms of the consequent-conse- 
quent. In the former the distributed middle is absolutely 
indispensable ; in the latter it is necessary only for guarded 
conclusions. 

Yet, in thus opposing syllogisms of the separating-conse- 
quents to those of the consequent-consequent, we really contrast 
one operation of the consequent-consequent with another ; the 
separating-consequents being equivalent to the consequent- 
consequent with the addition of a conversional contradiction. 
Our teaching, here, is not inconsistent with the doctrine that 
the consequent-consequent is the fundamental principle of 
catenate inference. It refers all syllogizing to this law as 
having, or as not having, that conversional addition. 

11. The fallacy which may result from two particular (or 
contingent) premises, is radically the same with that of the 
undistributed-middle. In syllogisms of the separating-conse- 
quents no conclusion whatever can follow two such premises ; 
because, in the second figure the major premise, and in the 
fourth the negative premise, must be apodeictic. Precisely 
the same reasons which demand a distributed middle require 
one premise at least to be universal. But in syllogisms of the 
consequent-consequent, if both premises be particular, a con- 
jectural conclusion is lawful; only a guarded conclusion is 
fallacious. This is the weaker form of the paralogism. 

Here, however, a particular affirmative, used as minor pre- 
mise in the first figure, if its predicate be distributed, must be 
regarded as an universal affirmative, and as really relegating 
the argument to the third figure. Tor, in saying, 

Some heroes are godlike ; 

Some men are all the heroes ; therefore 

Some men are godlike, 

the minor premise means "all heroes are men," is apodeictic 
in effect, and justifies the guarded conclusion. This shows 



Chap. XXVII. ] FALLACIES OF CATENATE INFERENCE. 317 

that the rule requiring one premise to be universal, in order 
to a guarded conclusion, signifies, speaking exactly, that the 
middle term must be distributed in one or other of the 
premises. 

12. The last fallacy to be named, as arising from false syllo- 
gistic construction, is the inference of an apodeictic conclusion 
if either premise be contingent. The self-evident truth, that a 
chain of connection cannot be stronger than its weakest part, 
applies to every mode of syllogizing. Accordingly, if we use 
the separating-consequents, which is conditioned on an uni- 
versal major premise, the minor must also be universal ; and 
if we use the consequent-consequent, both premises, likewise, 
must be universal ; if the conclusion is to be universal. 

Indeed, normally, universal affirmative conclusions not only 
require two apodeictic premises, but also that these be so 
related to each other, that the antecedent of the minor may 
become the antecedent of the conclusion, and the consequent 
of the major the consequent of the conclusion. Hence, that- 
form of proposition, which is the most important of all, the 
universal affirmative, is provable properly only in the first 
mood of the first figure. 

Such, then, are the fallacies in syllogistic connection, whether 
arising from too many terms, or ambiguous terms, or negative 
premises, or undistributed terms, or particular premises. 



318 THE MODALIST. [Chap. XXVIII. 



CHAPTER XXVIII. 

EXTERIOR CATENATIONAL FALLACIES. 

1. Exterior catenational fallacies are of two modes, (a) the petitio prin- 
cipii and (b) the ignoratio elenchi. 2. The direct petitio is called the non- 
causa, and also "the false, or fictitious, middle." 3. Specific forms of it 
are the non-tale pro tali; and the post-hoc, ergo propter hoc. 4. The 
indirect petitio includes (a) the implicatio mendax, (6) the circulus in 
probando, and (c) the saltus in deducendo. 5. The ignoratio may take 
place either with or without intention. Often accompanies a shifting of 
of the ground. The elenchi mutatio. The argumenta ad hominem, ad 
populum, ad verecundiam. 6. Fallacies "in dictione" and "extra dic- 
tionem," — a superficial distinction. 

1. As already stated, there are modes of paralogism by 
which a conclusion can be wrongly supported even while there 
may be a correct catenation of sequences. Though one's syllo- 
gism be perfect, his argument will be worthless, if either his 
premises be unreliable, or if he prove something different from 
that which he ought to prove, and which is the point at issue. 

The first of these sophisms is known as the petitio principii, 
or "begging of the question"; the second, as the ignoratio 
elenchi, or the irrelevant conclusion. In both of the Latin 
names there is reference to a question as under debate ; this 
indicating that these fallacies occur more frequently in dis- 
cussions of long standing, than in new investigations. 

The phrase " petitio principii " means the illicit assumption 
of some principle, or ground of inference ; and intimates that 
this mode of paralogism, though it begs the question, does not 
immediately assert the point at issue. An immediate asser- 
tion could scarcely be fallacious, because it would not have 
even the appearance of argument. 

2. The petitio may be denned as the paralogism of false 
assumption. This, however, does not signify that the premise 
may not be true, but only that it is unwarranted. 



Chap. XXVIII. ] EXTERIOR CATENATION AL FALLACIES. 319 

Xo premise can be fallaciously asserted without some show 
of reason ; and this appearance may either appeal formally to 
our faculties of knowledge, or may be supported by concealed 
implications. There are, accordingly, two general modes of 
the petitio, the direct and the indirect. 

The former of these is the more common and important ; 
and is known by the name " non-causa pro causa" In this 
expression the word " causa " must be taken, in a broad, logical 
sense, to denote an antecedent, or ground of inference ; whether 
it be an efficient cause or not. Logic does not consider effi- 
cient causes as such. The "non-causa" is a syllogism, in 
either premise of which something is falsely assumed to be 
the antecedent of a given consequent. 

This paralogism is also called, more technically, "the false, 
or fictitious, middle" ; and is thus contrasted with the ambigu- 
ous, and with the undistributed, middle. For, from the nature 
of the case, if either premise, or both, be falsely assumed, the 
middle term must be falsely used either as subject or as pred- 
icate or as both. 

There is also another reason for this second designation. 
The middle, or connecting, term, is, in a pre-eminent sense, the 
cause, or ground, of the conclusion ; to fxev atrtov to /xeVov, says 
Aristotle (" Analyt. Post.," II. 2). Hence, if the middle, either 
as antecedent or as consequent, be fictitious, there is really 
nothing — no reason — to produce conviction. 

Should we say, " The magnet is animated, because it moves 
itself," there would be a non-causa, or fictitious middle, on the 
supposition that the implied major, "Whatever moves itself 
has life," is not true, or not evident. And, even were this 
allowed to be true, there would still be a fictitious middle unless 
there were reason to believe that "magnets move themselves." 

3. Specific forms of the non-causa have received specific 
names. When the false premise is supported by a superficial 
resemblance, but has no true analogy, to some known sequence, 
it is styled the "non-tale pro tali" ; as, for example, that "a 
bat must lay eggs ; because it has wings, and flies." Also, if, 
without any true reasoning about causes, a general law is 
asserted simply because one event has, more or less frequently, 



320 THE MOBALIST. [Chap. XXVIIL 

preceded another, the fallacy is designated the "post hoc, ergo 
propter hoc" ; as that "protection (or free-trade) must be a 
good policy, because countries have prospered under it." They 
may have prospered despite of it. 

4. We now pass to those forms of the petitio, which employ 
the aid of indirection and concealment. They are three in 
number ; and may be named the fallacies of the false implica- 
tion, of reasoning in a circle, and of the gap in argument ; or, 
using Latin terms, the implicatio mendax, the circulus in pro- 
bando, and the saltus in deducendo. 

The unfair implication is the device of those who do not 
immediately assert a falsehood, but tell things, or raise ques- 
tions, which presuppose the falsehood, as if it were true. 
When the words of such persons are made plausible by reason 
of an ingenious accommodation to facts, this method of deceit 
often proves successful. It is a favorite instrument of polit- 
ical warfare 5 and appears in those lying inventions which 
demagogues circulate, to deceive the public concerning tha 
character of statesmen and the designs of parties. 

That mode of the implicatio mendax which logicians notice 
most, is rather amusing than important. It is the fallacy of 
the second, or implicating, question (sophisma heterozeteseos — 
fallacia plurium interrogationum) . An ancient example of it, 
named the "cornutus," employs the query, "Have you cast 
your horns ? " This is really a second question, which implies 
that the prior enquiry, " Have you had horns ? " can be 
answered affirmatively. Hence, if one replies that he has not 
cast his horns, it will be said, " Then you have them yet ! " 
while, if he says that he has cast them, it can be said, " Then 
you were once a horned animal ! " 

A specific mode of the heterozetesis, is the fallacia plurium 
interrogationum, in which several disconnected questions are 
asked together j as if all could be answered at once and in the 
same way. In saying, " Are honey and gall sweet ? " it is 
presupposed that these substances have the same taste, what- 
ever that may be. This presupposition must be rejected as 
unwarranted ; after that, the enquiry can be answered as two 
questions. 



Chap. XXVIII. ] EXTERIOR CATENATION AL FALLACIES. 321 

All paralogisms of the heterozetesis are refuted by showing 
that a false implication, attached to the nature of the question, 
renders a categorical answer absurd and illogical. 

The circulus in probando arises when a premise is at first 
reasoned from hypothetically, and then afterwards proved by 
using the conclusion itself as a premise. Thus a speaker 
might argue that a policy is wise, simply because it works well, 
without giving sufficient evidence regarding its working; and 
afterwards that it must work well, because it is wise. The 
defect of such a procedure is commonly concealed by length 
of argument and new forms of expression. 

The " saltus" or leap, in ratiocination, occurs when some 
sequence, in a series, does not really follow upon the pre- 
ceding one, yet is assumed to do so. Such an argument 
employs a succession of middle terms, each of which is conse- 
quent to a foregoing, and antecedent to a following, term. The 
confessed absence of one of these connections would rob the 
reasoning of all logical force ; evidently, therefore, the saltus, 
when analytically stated, must participate in the nature of 
the fictitious middle, or non-causa. Indeed, speaking broadly, 
this latter paralogism would include every mode of the petitio. 
But the saltus is distinguished specifically from the non- 
causa proper, because the fallacy of it is hidden in the midst 
of a succession of inferences, most, or all, of which may be 
correct. 

5. The last general mode of fallacy to be discussed is the 
ignoratio elenchi, or irrelevant conclusion: This takes place 
when somehow the question at issue is misstated, and a con- 
clusion proved different from that really required. 

Often this paralogism is preceded or accompanied by a 
" shifting of the ground " of the argument ; either with or with- 
out, intention. For, although the same proposition may be 
maintained on different grounds, a change in reasons some- 
times indicates that the conclusion first attempted is being 
abandoned for another. 

When the ignoratio happens inadvertently, it is called "miss- 
ing the point " ; but it is frequently a piece of sophistry. In 
either case there is an aptness in the word " ignoratio " ; for 



322 THE M0DAL1ST. [Chap. XXVIII. 

this suggests a mental activity in the rejection of knowledge, 
which is more than simple " ignorantia," or ignorance. 

"Elenchus" (t'Aeyxos) originally signified the proposition 
to be maintained in refutation of an adversary — the contra- 
dictory of his assertion — and then came to mean, in general, 
the conclusion to be proved, the question at issue. 

The ignoratio takes place, not only when the substituted 
conclusion is entirely new, but also when part only of an 
assertion is proved, as if it were equivalent to the whole ; for 
example, that a man was influenced by money, and (being so) 
was mercenary; or that he killed another, and (in doing so) 
committed murder; or that some measure is open to certain 
objections, and should be rejected (no proof being given that 
the disadvantages outweigh the advantages). 

The point in dispute is sometimes altered at the beginning 
of a discussion; more frequently this change takes place 
during the course of debate ; in which case we may use the 
specific name, " elenchi mutatio" or a change of the question. 
This substitution may occur through mere confusion of thought 
in abstruse discussions ; but it is chiefly to be found in the 
reasonings of those who wish to have some controversy de- 
cided apart from its true merits. Thus the argumentum ad 
hominem seeks to confound an adversary by showing his incon- 
sistency, selfishness, or want of principle, instead of proving 
the unworthiness of his cause. Such reasoning is opposed to 
the argumentum ad rem, or ad judicium. It is never admis- 
sible in judicial proceedings ; and can be permitted in political 
discussions only when the public interests require the exposure 
of incompetent and unreliable leadership. 

The argumentum ad populum and the argumentum ad vere- 
cundiam are also, for the most part, mere sophistries. The 
former of these is a demagogic appeal to vanity and ignorant 
prejudices, in a case where the requirements of justice and 
right should be presented ; the latter excludes arguments 
based on truth, by urging the respect due to persons of reputa- 
tion or authority. So, also, the argumentum ad ignorantiam is 
a demand that some opinion shall be accepted, because one's 
adversary has nothing better, or more plausible, to offer. All 



Chap. XXVIII.] EXTERIOR CATENATIONAL FALLACIES. 323 

these forms of the mutatio are mentioned by Mr. Locke, in the 
fourth book of his essay (Chap. XVII.). 

6. In the chapters which are now brought to a close, we 
have not referred to a distinction made by Aristotle, and 
adopted by many logicians as a basis for their discussions con- 
cerning fallacies. It signalizes the fact that the deceptive 
power of some paralogisms depends partly, or wholly, on forms 
of verbal expression; while that of others is independent of 
this, but arises exclusively from the character of the thought 
employed. Aristotle, accordingly, distinguished fallacies in 
dictione from fallacies extra dictionem. 

This division is useful as reminding us that frequently, in 
order to refute a paralogism, it is necessary to define the 
meaning of words and the force of constructions, while, in 
other cases, this work is not needed, but only a determination 
of the thought. At the same time, the distinction is too super- 
ficial to form a basis for thorough exposition. For, after 
language has been explained, fallacies in dictione are found to 
resolve themselves into fallacies extra dictionem. 



INDEX AND VOCABULARY. 



This index gives the name of every author mentioned in the foregoing discussions, 
and the number of every page on which he is mentioned. 

It is also designed to assist the student, who may be interested in any particular 
point, or question, to trace the teachings of the book respecting that point, as these may 
present themselves in the successive chapters. In other words, it is offered as a kind of 
concordance. 

In addition, the intention has been to include every technical logical term, with refer- 
ences to the pages on which its meaning is explained; and, in this way, to furnish a 
defining vocabulary. 

For further information respecting metaphysical terms, or topics, especially as related 
to the perceptionalist philosophy, the reader is referred to the author's " Human Mind '* 
and " Mental Science." 



Abstract, the term, 46. 

Abstraction, distinguished from gen- 
eralization, 37. 

Accent, fallacy of, 307. 

Accident, as a " predicahle," separable 
and inseparable, 58. 

Accident, as opposed to substance, 35, 
58. 

Accident, fallacy of, genuine and spu- 
rious, 308. 

Accidents of entity, 121. 

Accidental definitions, 63. 

Action (n-olen/) as a category of predi 
cation, 50. 

Actualistic belief and assertion, 24, 87, 
104, 150. 

Adjunct, defined, 59. 

Affirmation, 81, 90, 93. 

Affirmative, the, does not always af- 
firm, 248-254, 310. 

Affirmative propositions, their conver- 
sion, 192-3. 

alo-drjo-ts, or perception, the basis of all 
knowledge, 300. 

11 All," collectively and distributively, 
43, 307. 

Ambiguous-middle, the, 306. 

Analogy, of natural sequences, 142; 
inference from, 172. 

Analytic judgments, 125. 

Animals, divided logically, 75, 76. 

Antecedent and consequent, the law 
of, 7, 9, 107, 111, 123, 131, 151, 152-3. 



Antecedent, exact and reciprocative, 
111. 

Apodeictic, or demonstrative, infer- 
ence, 23, 108, 150. 

Applicative inference, 131, 140, 152, 
226, 303. 

Apprehension, simple, 33. 

Arg amentum, ad rem vel judicium, 
ad hominem, ad populum, ad vere- 
cundiam, ad ignorantiam, 322. 

Aristotle, his organon, 2; his modal 
propositions and syllogisms, 97, 101, 
241 ; his definition of judgment and 
the proposition, 6, 82; on contin- 
gency, 8 ; his definition of the syllo- 
gism, 10, 222 ; his categories of pred- 
ication, 46 ; his use of the term, ouo-i'a, 
48; on species and definition, 54; on 
genus and difference, 55, his distinc- 
tion between the internal and the 
external word, 84 ; his use of the 
term "categorical," 85; interprets 
"not" to signify separation, 90; 
defines necessity, 110; on the origin 
of knowledge, 119, 300 ; on the law 
of contradiction, 126 ; on paradig- 
matic inference, 132 ; on final causes, 
144; his four causes, 144; discusses 
only three syllogistic figures, 236 ; 
prescribes no order of syllogistic 
statement, 240; his dictum, 263; his 
reduction of syllogisms, 282-6; on 
example and induction, 299; on first 
325 



326 



INDEX AND VOCABULARY. 



principles, 300; on the middle term, 
300, 319; his division of fallacies, 
323; vide "Mental Science." 

Art, the term as applied to logic, 13, 
16, 26. 

Ascript, ascripta, defined, 36, 48, 26 

Ascriptional predications, 50, 92, 268. 

Asserted-consequent, the, 194, 200, 243, 
252. 

Assertion, defined, 80, 153. 

Assertivity, 93. 

Assertory, a term used by Kant, 98. 

Attribute, defined, 59. 

Axioms, 121, 133 ; syllogistic, 262-7. 

" Begging the question," 318. 

Being, or entity, 51, 58. 

Belief, or conviction, 21, 79. 

Binomial formula, the, in the calcula- 
tion of probabilities, 168. 

Bowen, Prof. Francis, on modality, 4, 
101. 

Canonics, the Epicurean name for 
logic, 174. 

Canons of experimental enquiry, 145. 

Categorematic and syncategorematic 
words, 34. 

Categorical propositions, 85, 88, 89, 
106, 174. 

Categories of Aristotle, the ten, 46. 

Category, defined, 46. 

Catenate inference, 227-8, 304; falla- 
cies in, 303-320. 

Cause and effect, the law of, 139, 
146. 

Certainty, moral, 172. 

Chances, defined, 9, 162; the ratio of 
the, 164 ; calculation of, 164-9. 

Cicero, the inventor of the word "es- 
sence," 67. 

Circulus in probando, the, 320. 

Class notion, the, 43. 

Clearness, defined, 61. 

Common-antecedent, the, 232, 251, 
265-6. 

Common-consequent, the, 250. 

Common-sense, doctrine of, 5. 

Comparison, 37. 

Composition, the fallacy of, 307. 

Compound assertions, 92. 

Conception, 31. 

Conceptualism, 38. 

Concrete, the term, 46. 



" Conditional " assertions and reason- 
ings, 81, 85, 89, 103, 106, 156. 

Conditionative, or modal, propositions, 
97, 99, 102, 106, 174. 

Conditions, doctrine of, 8, 104, 109, 110, 
111, 131. 

Conditions, necessitant, or logical, 111. 

Confliction ; see contrariety. 

Conjugation, or syzygy, of syllogisms, 
240. 

Consequent-consequent, the, 229, 259, 
263, 279. 

Consequent, the asserted, 194, 200, 243, 
252. 

Contingency, 8, 9, 24, 101, 117, 180, 183, 
197, 204, 292, 298. 

Contingency, in the wide sense and as 
including possibility, 101, 183, 189. 

Contingency, half-guarded, 182, 186, 
197, 208, 218, 246, 264; unstable, or 
unguarded, 184, 209, 219, 248, 258, 
273 ; guarded, 185, 314 ; encouraging 
and discouraging, 187 ; empirical and 
mathematical, 198, 207, 210, 264; 
fixed, or embedded, 220. 

Contingent syllogisms, 244, 248, 289. 

Contradiction, the law of, 121, 126, 128. 

Contradiction, consequential and cate- 
gorical, 156, 157. 

Contradictory opposition, 177, 182, 
187; in a wide sense includes con- 
trariety, 155. 

Contradictories, are conceivable only 
in pairs, 158. 

Contraposition, explained, 127, 193, 
203. 

Contrariety, 154, 157, 176, 180, 296. 

Conversion, logical, 190; of necessary 
sequences, 111; ground for, 125; of 
particular negatives, 193. 

Conversion per accidens, or by the 
asserted consequent, 194, 200, 243, 
280, 283 ; per differ entiam, or by the 
retained-necessitant, or differential 
conversion, 194, 200, 244, 280, 315; 
" simple," 194: by negational exclu- 
sion, 194; by the denied-consequent, 

200, 243, 280, 313; of contingency, 

201, 211, 215; as related to the law 
of reason and consequent, 243, 

Conviction, 22, 79. 
Co-ordination, logical, 76. 
Copula, origin and use of the verb "to 
be," as 89; vide "Mental Science." 



INDEX AND VOCABULARY. 



327 



Cosrnological judgments; vide "Men- 
tal Science." 

Creational development, a possible 
theory, 143. 

Criticism, scientific, 140. 

Deduction, 133. 

Definite and indefinite notions, 42. 

Definitions, 54, 61, 67 ; distribute the 
predicate, 96. 

De Morgan, Prof., his definition of 
logic, 14. 

Demonstration, 23, 108, 150. 

Denial, 153. 

Denied-consequent, law of, 157, 200, 
243, 282. 

Design in nature, 144. 

Dichotomy, as a mode of division, 
78. 

Dictum of Aristotle, the, 262. 

Difference, individual or numerical, 
40,56; specific, 40; as a predicable, 
55 ; vide " Mental Science." 

Dilemma, the, constructive and de- 
structive, 160. 

Discourse of reason, 18. 

Disjunction, logical, 77, 154, 159, 256, 
296. 

Disjunctive syllogism, 159, 296. 

Distinctness, as a quality of thought, 
61. 

Distribution, the, of a notion, 43, 93. 

Division, the fallacy of, 307. 

Division, logical, not didactive nor 
rhetorical, 30, 72; a synthetic proc- 
ess, 71; rules of, 72-77; expressed 
by a predication , 96. 

Dogmatic, the term, 98, 242, 261. 

Elenchi mutatio, 322. 

Elenchus, denned, 322. 

Embedded contingency and possibility, 
183, 220. 

Enthymeme explained, 275. 

Entity denned, 31, 51. 

Enumeration, simple, 302. 

Enunciation, as distinguished from as- 
sertion, 80. 

Epicheirema, the, 275. 

eTrto-rrjuTj, always true, according to 
Aristotle, 297. 

Epi syllogism, 278. 

Error, origin of, 290. 



Essence, 55, 67 ; singular, 69 ; the nom- 
inal and the real, 69. 

Essential and accidental definitions, 62. 

Euler's symbolic diagrams, 268. 

Excluded-middle, the law of the, 121, 
128. 

Exclusive and exceptive assertions, 97. 

Exercises in constructing and reducing 
syllogisms, 287. 

Existence and non-existence, 31, 153. 

Experience, or zy.irei.pLa, as including 
every immediate perception, 300; 
for other meanings of the term see 
the author's " Mental Science," 
Chap. XLIX. 

Fact is both positive and negative, 32. 
Factual propositions, 103, 261; their 

conversion, 190. 
Fallacies, 290; formal and material, 

305 ; in dictione and extra dictionem, 

323. 
False, or fictitious, middle, 319. 
Falsity, or untruth, an ambiguous ex- 
pression, 291. 
Figures of syllogism, the, 238, 248, 262, 

279. 
Figure, the fourth, 238, 254, 262, 267, 

281 ; as compared with the others, 

259, 282, 311-314. 
Final cause in nature, 144. 
Form and matter, 68; vide "Mental 

Science." 
"Formal" logic, 28. 
Formal or schematic notions, 33. 
Fundamentum, the term, 74, 75. 

Gases, logically divided, 75. 

Generalization, denned, 37; the prin- 
cipiative, 132. 

General notion, 37. 

Genus, as a predicable, 53, 55, 155, 
159 ; the predication of it not neces- 
sarily analytic, and either individual 
or general, 53. 

Goclenius, Rudolphus, professor in 
Marburg, his form of the sorites, 277. 

God, causally unconditioned, yet logi- 
cally necessary, 110 ; vide " The 
Human Mind," Chap. XXI. 

Guarded and unguarded contingencies, 
182, 186, 197, 208, 218, 246, 248, 249, 
253, 255, 258, 281-3. 



328 



INDEX AND VOCABULARY. 



Hamilton, Sir William, his definition 
of logic, 3 ; his quantification of the 
predicate, 95 ; on modal proposi- 
tions and syllogisms, 262 ; his syllo- 
gistic notation, 270; his doctrine of 
the syllogism, 274. 

Historical, or factual, propositions, 103. 

Homologic inference, 7, 18, 130, 150, 225. 

Hypothesis, the inductive, 139. 

Hypothetical, or suppositive, judgments 
and propositions, 24, 87, 103; vide 
"Mental Science." 

Hypothetical syllogism, the, 150, 151, 
156, 228, 294. 

Idea, now used as equivalent to notion, 
or conception, 31. 

Idealism, defined, 39. 

Identity, the law of, 121, 124, 128, 190. 

Identity, numerical and specific, 41. 

Ignoratio elenchi, 318. 

Illation, or inference, and illative, or 
inferential, 7, 98, 103. 

Immediate, or intuitive, knowledge, 
138, 290; vide " Mental Science." 

Implicatio mendax, the, 320. 

Impossibility, 99, 100, 113, 186, 298. 

Indefinite notions, 42 

Indefinite quantity, 94. 

Individuals and individual notions, 
40-44. 

Induction, 132 ; the act, 136 ; the proc- 
ess, 137 ; canons of, 145 ; the induc- 
tive syllogism, 300. 

Inference, and inferential propositions, 
6, 103, 105, 150; immediate, 108, 119, 
293. 

Inherential propositions, 82. 

Intuition, 18; vide "Mental Science." 

Irrelevant conclusion, 321. 

Judgment discussed, 6, 79. 

Kant, Immanuel, his views on logic, 1 ; 
his definition of judgment, 6; his 
term "assertory," 98. 

Knowledge, or absolute and well- 
founded conviction, a species of 
judgment, 79; vide "Mental Sci- 
ence." 

Lambert, an excellent German logi- 
cian, 270. 

Leibnitz, Gottfried Wilhelm, on the 
category of substance, 47. 



Linnaeus, his definition of man, 63. 

Locke, John, his definition of judg- 
ment, 6, 22, 83; of reason, 17 ; on the 
category of substance, 47; on the 
nominal, and the real, essence, 69; 
on substance, 70 ; on the origin of 
knowledge, 119 ; on immediate infer- 
ence, 119 ; on certain fallacies, 322. 

Major, minor, and middle terms, 
238. 

Mark, the added, as the basis for logi- 
cal division, 75. 

Mathematical principles, 122; infer- 
ence, 297. 

Matter, in logic, 68. 

Maxims of inductive conjecture, 141. 

"May" and "may not," 182. 

McCosh, James, Pres., quoted, 21. 

Mediate and immediate inference, 108; 
as a distinction in relational infer- 
ence, 224. 

Mental and verbal propositions, 84, 86, 
95, 103. 

Metaphysical first principles, 122. 

Metaphysics, or ontology, the basis of 
logic, 4, 120. 

Methodology, defined, 27. 

Methods, of agreement, of difference, 
etc., 146-9. 

Mill, John Stuart, on inductive meth- 
ods, 146 ; on contingency and proba- 
bility, 207. 

Mnemonic lines of Petrus Hispanus, 
the, 283. 

Modal, or conditionative, predications, 
97; as contracted with the pure or 
dogmatic, 102, 106 ; essentially illa- 
tive, 174. 

Modalist, reason for this name, 4. 

Modality, 10, 101, 106, 150, 242, 262. 

Modus ponendo ponens and tollendo 
tollens, 153; tollendo ponens and 
ponendo tollens, 159, 294. 

Moods, syllogistic, 11, 240, 242, 262, 
287 ; their symbolic notation, 270. 

Mortgage investments, 77. 

Nature of a thing, the, 55, 59. 

Nature, or the universe, the intellectu- 
ality of, 141-4. 

Necessity, 99, 180; logical, 101, 113, 
186; its converse, 199; vide "Mental 
Science." 



INDEX AND VOCABULARY. 



329 



Necessitant, the retained, 194, 244, 247, 
253; condition, the, 111. 

Negation, 81, 90, 93. 

Negative propositions, 94; must some- 
times be construed as affirmatives, 
245, 252, 254, 310. 

"No," the adjective, 94. 

Nominal and real definitions, 66. 

Nominalism, 39. 

Non causa pro causa, the, 319. 

Non-existence and the non-existent, 32. 

Non tale pro tali, 319. 

''Not," the particle, 91, 95. 

Notational definition, the, 65. 

Notion, the, an idea, or conception, 
named from its relation to knowl- 
edge, 31. 

Osject, objectivity, objectuality, 31. 
Ontology, as related to logic, 4, 120, 

301. 
Opposition, logical, 174, 179. 
ova-ia, substance, or essence, 46. 

Paradigmatic inference, 131, 299. 

Paralogism, defined, 290. 

Parsimony, the "law" of, 143. 

Particular propositions, 269; categori- 
cal and modal, 93, 175, 196, 197. 

Perceptionalism, defined ; vide " Men- 
tal Science." 

Perceptions, simple and immediate, 
free from error, 290. 

"Per se" and "per accidens" ex- 
plained, 285. 

Petitio principii, the fallacy of, 316. 

Place, or position, as a category of 
predication, 49. 

Plurium interrogationum, the fallacy, 
320. 

Poly syllogism, defined, 278. 

Ponendo ponens and ponendo tollens, 
153-9. 

Positing, or assertion, of a statement, 
the, 153. 

Position, or posture, as a category of 
predication, 50. 

Possession, or condition, as a category 
of predication, 50. 

Possibility, 113, 173, 205, 293; as in- 
cluding contingency, 99, 115; em- 
bedded, 114, 183 ; unstable, 184. 

Possible to be, the, 113; and the possi- 
ble not to be, 115. 



Post hoc, ergo propter hoc, the fallacy 

of, 317. 
Postulates, 121, 133. 
Predicables, the five, defined, 52 ; their 

use, 59. 
Predicate, defined, 35, 85, 89, 95. 
Predication, 80, 83 ; grammatical, dis- 
tinguished from logical, 84; force of 

categorical, 95. 
Predicative notions, 34, 45. 
Premises defined, 237; order of, 240; 

false conclusion from true, etc., 291. 
Presentational perceptions, 23. 
Presentential propositions, 82, 87. 
Principiative inference, or principi- 

ation, 131, 226, 300. 
Principle, the term, 73; principles of 

inference, 119, 133. 
Principium individuations, 41. 
Probability, 99, 116; conditioned on 

possibility, 100; its oppositions, 189; 

ordinary and philosophical, 170; 

orthologic and homologic, 171; the 

calculation of, 164-9; vide "Human 

Mind," Chap. XXIV. 
Problematic inference, 23, 108, 150, 

292, 298. 
Property, as a predicable, generic, and 

specific, 57. 
Propositions, 79-88, 104. 
Proprietal conceptions, 58. 
Prosyllogism, 278. 
Pure, the term, 28, 98, 242. 
Pure, or dogmatic, propositions, 97, 

98, 242, 261; verbal in character, 

102; as related to modal, 106; pure, 

or dogmatic, syllogisms, 261. 

Quality, as a category of predication, 

48. 
Quality, as a predicable, 60. 
Quality of propositions, the, 81, 93, 175. 
Quantity, as a category of predication, 

48. 
Quantity of propositions, the, 93: a 

kind of added predication, 102, 175. 
Quantification of the predicate, 92, 

274. 
Quantification of modals, the, 195. 

Ratio of the chances, the, 100, 116, 162, 

198, 298. 
Ratiocination, or reasoning, 108. 
Real definitions, 66. 



130 



INDEX AND VOCABULARY. 



Realism and Nominalism, 39, 41; vide 
" Mental Science." 

Reason, the faculty of, 16; the intui- 
tive and the discursive, 17. 

Reason and consequent, the law of, 7, 
9, 10, 107, 131, 152, 260. 

Reasoning, 108; in the general, 134; 
inductive, 136. 

Reciprocating necessities, 95, 111. 

Reciprocation, the law of syllogistic, 
233, 267. 

Beductio ad absurdum, 127, 287. 

Reduction of syllogisms, 278; new 
method of, 282; indirect reduction, 
283; per impossibile, 286. 

Reid, Dr. Thomas, on modal syllo- 
gisms, 262. 

Relation, as a category of predication, 
49; vide "Mental Science." 

Relations, logical, or necessary, 110. 

Relational, or adjunctional, defini- 
tions, 63. 

Relational inferences and syllogisms, 
223, 293, 296. 

Representative essence, the, 68. 

Retained-necessitant, the, 194, 244, 281, 
315. 

Saltus in deducendo, 320. 
Schematic notions, 33. 
Scholastic definition, the, 65. 
Separate, and catenate, inference, 290, 

304. 
Separating-consequents, the law of the, 

230, 249, 260, 265, 279. 
Shifting the ground of argument, when 

fallacious, 319. 
Simple and compound assertions, 92. 
Simplicity of Nature, the, 144. 
Singular notions, 42, 69. 
Singular propositions, really have no 

" quantity," 94. 
Solidity, primary perception of, 139. 
Sophisma heterozeteseos, the, 320. 
Sophistry, involves the intention to 

deceive, 290. 
Sorites, the, 275 ; the Goclenian, 277. 
Species, the predicahle, sets forth the 

whole nature conceived of, 54; as a 

class-name, 155. 
Specific difference, 40; may, like genus, 

be either individual or general, 53. 
Sphere of logic, the, 3, 25. 
Square, the logical, 176. 



Stoic doctrine of final cause, the, 144. 

Subcontrariety, 178, 188. 

Subordination, or subalternation, of 
propositions, 125, 176, 177, 181, 184. 

Subject, the term, 20, 35, 85, 89. 

Subjective and predicative notions, 34. 

Subjectual, the term, 20. 

Sublation, defined, 153. 

Substance, as a category of predica- 
tion, 45; vide "Mental Science." 

Substance and accident, as correspond- 
ing to subject and predicate, 35, 58. 

Substance, metaphysical; vide "Men- 
tal Science." 

Substanta and ascripta, 36, 45, 51, 69. 

Substantal predications, 50, 92, 125, 
268. 

Substantal and ascriptional predicates, 
60. 

Substantialization of ascripts, 51, 191, 
268. 

" Substantial form," 69. 

Substitutional judgments, based on the 
law of identity, 124. 

Sumption and subsumption, 294, 303. 

Superalternation ; see subalternation. 

Supposition, or hypothesis, 139. 

Suppositive, or hypothetical inference, 
distinguished from the hypothetical 
syllogism, 151. 

Syllogism, the Aristotelian, 7, 10, 135. 

Syllogism defined, 222, 292; the syllo- 
gism proper, 7, 223, 228, 237, 274; 
the disjunctive, 159, 294-5; the 
translative, or hypothetical, 151, 228, 
294 ; the relational, 223, 296 ; the par- 
adigmatic, 225, 299; the principia- 
tive, 226, 299; the inductive, 136, 
300 ; the applicative, 226, 303. 

Symbolization of contingencies, 220. 

Syncategorematic words, 34. 

Synthetic judgments follow the prin- 
ciple of identity, 124. 

Synthetic order of premises, the, 240, 
278. 

Terms, or extremes, 237 ; middle, ma- 
jor, and minor, 238. 

"The," as article, sometimes has a 
distinctive, without a singularizing, 
force, 38. 

Theophrastus, the immediate successor 
of Aristotle : his use of the term 
" categorical," 85. 



INDEX AND VOCABULARY. 



331 



Thought, or conception, and belief, or 
conviction, the primary powers of 
mind, 21; vide "Mental Science." 

Tollendo tollens, 153; and tollendo 
ponens, 159. 

Transfer, the principle of logical, 151, 
154, 294. 

Truth, defined, 18 ; hypothetical, 150. 

Tychologic principle, the, or ratio of 
the chances, 162. 

Unasskrted-middle, the fallacy of 

the, 309. 
Uncontradicted-middle, the fallacy of 

the, 309. 



Undistributed-middle, the, 311. 

Uniformity of natural operations, 142. 

Unital, the term, 41, 94. 

Unity, or oneness, defined, 40. 

Universals, impossible entities, 39; 
vide " Mental Science." 

Universal propositions, 93; their con- 
version, 192; modals, 195, 196. 



Verbal and mental propositions, 84, 
86, 95, 103. 

Woolsey, Pres. Theodore D., his 
divisions of international law, 72. - 



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